Mathematical Sciences Research Institute Annual Report for 2010–11

Home , Akshay Venkatesh, Alan Edelman, Andrei Okounkov, Andrew Granville, Audrey Terras, Bjorn Poonen

Annual Progress Report on the Mathematical Sciences Research Institute 2010–11 Activities supported by NSF Grant DMS–0932078 May, 2012

1. Overview of Activities ...... 1 1.1 New Developments ...... 1 1.2 Summary of Demographic Data for 2010–11 Activities ...... 5 1.3 Scientific Programs and their Associated Workshops ...... 7 1.4 Scientific Activities Directed at Underrepresented Groups in Mathematics ...... 9 1.5 Summer Graduate Schools (Summer 2010) ...... 9 1.6 Other Scientific Workshops ...... 10 1.7 Educational & Outreach Activities ...... 11 a. Circle on the Road Spring 2011 (NSF Supplemental Grant DMS-0937701) b. Critical Issues in Mathematics Education Spring 2011: Math Education of Teachers (NSF Supplemental Grant DMS-0937701) 1.8 Programs Consultant List ...... 12

2. Program and Workshop Data...... 13 2.1 Program Participant List ...... 13 2.2 Program Participant Summary ...... 13 2.3 Program Participant Demographic Data ...... 14 2.4 Workshop Participant List ...... 16 2.5 Workshop Participant Summary ...... 17 2.6 Workshop Participant Demographic Data ...... 18 2.7 Program Publication List ...... 21 2.8 Program Publication Work-In-Progress List ...... 26 3. Postdoctoral Program ...... 27 3.1 Description of Activities ...... 27 3.2 Postdoctoral Fellow Placement List...... 39 3.3 Postdoctoral Fellow Participant Summary...... 40 3.4 Postdoctoral Fellow Demographic Data ...... 41 3.5 Postdoctoral Research Member Placement List ...... 44 3.6 Postdoctoral Research Member Summary ...... 44 4. Graduate Program ...... 44 4.1 Summer Graduate Schools (SGS) ...... 44 4.2 Summer Graduate School Data ...... 46 4.3 Program Associates ...... 50 4.4 Program Associates Data ...... 51 4.5 Graduate Student List ...... 54 4.6 Graduate Student Data ...... 54 5. Undergraduate Program (MSRI-UP) ...... 55 5.1 Description of Undergraduate Program ...... 55 5.2 MSRI-UP Data ...... 57

6. Brief Report of Activities in 2011–12 ...... 59 7. Appendix – Final Reports ...... 78

Program Reports No. 259: Random Matrix Theory, Interacting Particle Systems and Integrable Systems No. 260: Inverse Problems and Applications No. 261: Free Boundary Problems, Theory and Applications No. 262: Arithmetic Statistics No. 266: Complementary Program 2010–11

Workshop Reports No. 508: Random Matrix Theory and Its Applications I No. 509: Connections for Women: An Introduction to Random Matrices No. 517: Random Matrix Theory and Its Applications II No. 513: Connections for Women: Inverse Problems and Applications No. 514: Introductory Workshop on Inverse Problems and Applications No. 540: Inverse Problems: Theory and Applications No. 562: Connections for Women: Free Boundary Problems, Theory and Applications No. 563: Introductory Workshop: Free Boundary Problems, Theory, and Applications No. 564: Free Boundary Problems, Theory, and Applications No. 565: Connections for Women: Arithmetic Statistics No. 566: Introductory Workshop: Arithmetic Statistics No. 567: Arithmetic Statistics No. 584: Hot Topics: Kervaire Invariant No. 575: SIAM/MSRI ws on Hybrid Methodologies for Symbolic-Numeric Computation No. 587: Workshop on Mathematics Journals No. 601: Circle on the Road Spring 2011 No. 596: Critical Issues in Math Education 2011: Mathematical Education of Teachers

Summer Graduate School Reports No. 580: Summer School on Operator Algebras and Noncommutative Geometry No. 556: Sage Days 22: Elliptic Curves No. 550: Probability Workshop: 2010 PIMS Summer School in Probability No. 552: IAS/PCMI Research Summer School 2010: Image Processing No. 551: Mathematics of Climate Change No. 553: Algebraic, Geometric, and Combinatorial Methods for Optimization

1. Overview of Activities

This annual report covers MSRI projects and activities that occurred during the first year of the NSF core grant DMS–0932078.

1.1 New Developments

This year, 2010–11, was a busy and exciting year at MSRI. We held four (4) one-semester programs: Random Matrix Theory, Interacting Particle Systems and Integrable Systems, Inverse Problems and Applications, Free Boundary Problems, Theory and Applications, and Arithmetic Statistics. It is fair to say that all programs were very popular and their workshops heavily attended. We also had a number of exciting additional workshops, such as Kervaire Invariant One (October 2010), MSRI’s annual Hot Topics workshop. In April 2009, Hill-Hopkins- Ravenel announced a solution to the Kervaire Invariant One problem. This resolved an almost 50 year old problem in topology, and their techniques and approach were quite different from anything previously attempted: They related the homotopical formulation due to Browder to equivariant homotopy computations. While it is one of the oldest branches of algebraic topology, equivariant homotopy theory (homotopy theory done in spaces endowed with an action of a fixed group G) is also one of the least understood. Many computations viewed as routine or elementary are simply unknown in the equivariant case, even for simple groups. One of the primary goals of the workshop was to make this rich branch of algebraic topology more accessible to topologists. Some of the highlights of the workshop were the talks given by Hill, Hopkins, and Ravenel themselves. A succinct and very interesting report can be found in the Appendix.

All programs had stellar researchers. Four (4) of them, Barry Mazur, Henryk Iwaniec, Percy Deift, and Gunter Uhlmann, were generously funded by the Clay Mathematics Institute ($100,000). Deift had just been elected (2009) to the National Academy of Sciences (NAS). Iwaniec, a member of the NAS since 2006, received the 2011 Leroy P. Steel prize for Mathematical Exposition. Mazur, a long time member of the NAS (1982) and of the American Philosophical Society (2001), had been a recipient of the Veblen (1965), Cole (1982), Chauvenet (1994) and Steel (1999) Prizes. Uhlman, a recently (2009) elected Fellow of the American Academy of Arts and Sciences, won both the Bocher and the Kleinman Prizes in 2011. Another fifteen (15) researchers, Manjul Bhargava, Henri Cohen, Jon Keating, Mikhail Feldman, Charles Elliott, Juan Luis Vazquez, Pierre van Moerbeke, Gerard Ben Arous, Herbert Spohn, Kari Astala, Margeret Cheney, Cristopher Croke, Graeme Milton, Plamen Stefanov, and Henrik Shahgholian were funded by MSRI’s Eisenbud Endowment and by a grant from the Simons Foundation.

Each of the programs had striking results to report. In fall 2010, the experimental work of Takeuchi and Sano, which demonstrated, for the first time, the occurrence of random matrix phenomena in nature, created quite a sensation. A breakthrough during the Inverse Problem program was achieved by Andras Vasy, who developed a new way of doing scattering theory for the Laplacian on Riemannian conformally compact spaces, including, in appropriate circumstances, non-trapping high energy bounds for the analytic continuation of the resolvent. During Spring 2011, one of the research highlights for the Free Boundary program was the work

1 of G.-Q. Chen, M. Bae, and M. Feldman on stability of Mach reflection configurations for steady compressible Euler systems. As for the Arithmetic Statistic program, Conrey, Iwaniec, and Soundararajan completed their work on the asymptotic large sieve, which they applied to prove the exciting result that the majority of `zeros' of every Dirichlet L-function obeys the Generalized Riemann Hypothesis. The Riemann hypothesis is considered by many mathematicians to be the most important unsolved problem in mathematics and is one of the seven Clay Mathematics million-dollar problems. Their proof, while not proving the Riemann Hypothesis, provides strong evidence in its favor.

Section 1.3 and the Appendix contain the detailed reports of all of our scientific programs and workshops. These contain a plethora of exciting discoveries and results.

Funding. We would also like to point out that in 2010-11, 35% of our programs costs were covered by private donations plus a grant from the NSA, while this ratio was 30% for our workshops. This well demonstrates MSRI's ability to leverage the support that the NSF provides and thereby amplify its benefits; we feel that this is possible because of MSRI's reputation for running programs of high quality.

Postdoctoral Program. In Spring 2009, the impact of the economic downturn had hit academia hard, causing hiring freezes and cancelled job searches. For mathematics, this represented a loss of some 400 positions for recent PhDs. The National Science Foundation, through its seven mathematics institutes (including MSRI), responded by creating new postdoctoral fellowships. This partnership resulted in the creation of 45 postdoctoral positions for young, highly-trained mathematical scientists from across the country. Ten of these fellowships were awarded by MSRI. Of those exceptional mathematicians, four, Tristam Bogart, Chris Hillar, Eric Katz, and Sikimeti Mau, participated in MSRI programs during the academic year of 2009–10 and continued on to their mentor’s institution, where they were supported throughout the 2010–11 academic year. Another six received one- and two-year fellowships allowing them to pursue their work at several institutions: Vigleik Angeltveit worked with Peter May at the University of Chicago for 2 years (2009-2011); Scott Crofts worked at UC Santa Cruz with Martin Weissman for 2 years as well (2009–11); Anton Dochtermann was awarded a one year (2010–11) fellowship to work with Gunnar Carlsson at Stanford University; Karl Mahlburg was at Princeton University working with Manjul Bhargava and Peter Sarnak (2009–11); Abraham Smith was at McGill University to work with Niky Karman (2009–11); and Jared Speck worked (2010–11) at Princeton University with Sergiu Klainerman. Aside from this special program, which ended in August 2011, about 30 Postdoctoral Fellows participated in our four scientific programs. Most were funded by MSRI’s NSF core grant, and two, Brooke Feigon and John Andersson, were funded by our Viterbi Endowment.

Each year, we poll the postdoctoral fellows that were in residence at MSRI two (2), four (4), and ten (10) years ago. Their comments are included in Section 1.9. Not surprisingly, there is a consensus among them that one of the great benefits of being a postdoctoral fellow at MSRI is the connections they were able to establish with the top researchers in their field as well as with fellow postdocs. Several credit these connections with having played an important role in their being hired at their current home institutions. Another important benefit of MSRI postdoctoral program is that the fellows have a unique opportunity to learn a lot from the leader in their fields. A striking further point was made in the comments this year: Many reported on the unique opportunity their MSRI postdoctoral fellowships gave them to branch out into areas that were

2 unknown to them prior to their visit to MSRI. We found this aspect very rewarding, for, undeniably, it is one of the harder skills to develop when one is a fresh Ph.D.

See details at http://www.msri.org/specials/nsfpostdocs, in Section 3, and in the Appendix.

Summer Graduate Schools. During the summer of 2010, MSRI funded a record number of graduate students. Eighty-four (84) institutions nominated a total of 205 students; of those, 188 attended one of six summer graduate schools. Two were held at MSRI and the four others were held at the University of Victoria in Canada, the University of Washington in Seattle, the IAS/PCMI in Park City and the NCAR in Boulder. For most of the summer graduate workshops, enrollment is based on a first-come, first-served policy. The workshops are so popular that some schools reach their maximum capacity within the first 24 hours. Detailed descriptions and reports for each of the SGS can be found in Section 4 and in the Appendix.

MSRI-UP program. This undergraduate research program is targeted at underrepresented minorities, with the goal of increasing their interest and enrollment in mathematics graduate programs. In the summer of 2011, the lead director was Suzanne Weekes, and the primary instructor was Professor Marcel Blais. Both were from Worcester Polytechnic Institute (WPI). The subject was Mathematical Finance, with project research in Liquidity Modeling and in Cointegration and the Capital Asset Pricing Model. One of the exciting moments of the school was the visit of Dr. Myron Scholes, the Frank E. Buck Professor of Finance, at the Stanford Graduate School of Business and a Nobel Laureate in Economic Sciences. Dr. Scholes, co- originator of the Black-Scholes options pricing model, was awarded the Nobel Prize in 1977 for his, then new, method of determining the value of derivatives. His informal talk electrified the undergraduates students, who had spent time mathematically preparing themselves for this talk. It should also be added that, to our amazement, they had put serious thinking into their dress code for Dr. Scholes visit!

Ricardo Cortez, one of the MSRI-UP directors and co-chair of MSRI’s Human Resources Advisory Committee, received the 2010 SACNAS Distinguished Undergraduate Institution Mentor Award. He was cited for his work with minority undergraduates, including his leadership in helping found MSRI-UP.

A detailed report of the MSRI-UP activities for the summer of 2011 can be found in Section 5 and in the Appendix.

Mathematics Journals: In February, MSRI had the pleasure of hosting the Workshop on Mathematics Journals, which featured many speakers giving their perspectives on the challenges that lie ahead for mathematics journals. It was organized by James M. Crowley (SIAM), Susan Hezlet (London Mathematical Society), Robion C. Kirby (University of California, Berkeley), and Donald E. McClure (AMS), and the speakers included working mathematicians, librarians, publishers, and a number of other individuals, all of whom contributed to a lively discussion on this subject that will affect all of us who create and use the mathematics literature. While it would be too much to expect everyone to agree on what policies the mathematics community should adopt, it was encouraging to hear the many constructive approaches that are being taken. Videos of many of the talks are on-line at MSRI's VMath web site, and the organizers have posted a `white paper' on the conference web page that summarizes the points of view that were represented.

Circle on the Road. During March 18–20, 2011, the Circle on the Road workshop took place at the University of Houston. The workshop included a mathematics festival that was open to the public. This event was part of the National Association of Mathematics Circles (NAMC), whose website includes a wide variety of materials designed to help mathematicians across the US to start math circles. Videos, lesson plans, problems, and solutions can be found on the NAMC website. Thanks to the generous support of the John Templeton Foundation, MSRI and the AMS are co-publishing books for the Mathematical Circles library.

Public Understanding of Mathematics. MSRI had quite a year of theatre and mathematics. In February 2011, MSRI hosted the playwrights of PlayGround for a discussion of how mathematicians think about number theory and culture. The playwrights each then had 9 days to write a 10-minute play that used the theme Kingdom of Number. The 20+ plays that were submitted were then judged by a panel consisting of mathematicians and theatrical producers, and the 6 best were given staged readings at the Berkeley Repertory Theatre on February 21. It was a nearly sold-out evening, and the six plays that were performed were well-received, continuing the tradition that MSRI night at PlayGround is one of the most successful PlayGround events each year.

Monologuist Josh Kornbluth. At the beginning of April, MSRI hosted the well-known monologuist, Josh Kornbluth, for two sold-out evenings during which he performed his monologue The Mathematics of Change, which tells the story of his stressful encounters with calculus during his freshman year at Princeton. It is a moving, thoughtful, humorous piece, and those who missed his live performances of this monologue can see it on the concert DVD, since the performances at MSRI in the Simons Auditorium were filmed. (Thanks to our donors Jerry Fiddler and David Fuchs for their support of this project, which will give a national audience a chance to see this work, as well as a chance to see MSRI on film.)

Andrew and Jennifer Granville, Anatomy of integers and partitions. At the end of April, 2011, MSRI (in conjunction with UC-Berkeley) hosted the play MSI: The Anatomy of Integers and Permutations, by Jennifer and Andrew Granville (theatre producer and mathematician, respectively). This highly original production, which teaches concepts in group theory and number theory through a murder mystery, received its West Coast premiere at MSRI, and perhaps we'll get a chance to see it filmed as well.

Mathematics of Planet Earth, MPE 2013. In scientific outreach, MSRI became one of the founding members of the Mathematics of Planet Earth 2013 program, which hopes to focus attention on the mathematical challenges inherent in addressing the global problems of sustainability, managing diseases and epidemics, management of resources, and studies of climate and its effect on life on earth. This program is, appropriately enough, global in scope, and MSRI is pleased to be a part of this consortium of mathematics institutes world-wide who are addressing these problems. More information about MPE2013 and MSRI's involvement can be found by going to the web site www.mpe2013.org.

Chicago Mercantile Exchange. We continue to cosponsor, with the Chicago Mercantile Exchange, the CME Group-MSRI Prize for innovation in financial mathematics and economics. The 2010 CME Group-MSRI Prize recipient was Jean Tirole, Scientific Director of Industrial Economics Institute and Member of the Toulouse School of Economics.

1.2 Summary of Demographic Data for 2010–11 Activities

During the academic year 2010–11, MSRI hosted 31 NSF Postdoctoral Fellows, 247 program members (members that came for a period of at least one month), and 1328 workshop participants.

The Postdoctoral program was particularly successful and is described in detail in Section 3. Of the Fellows, 23% were female, 29% were U.S. Citizens or Permanent Residents, and 52% listed a U.S. university as home institution. Of those institutions, 19% are located in the Northeast, 31% in the West, 13% in the Midwest, and the remaining 37 % in the South.

MSRI had a total of 247 long-term members. Members spent an average of 63 days at MSRI, with peak attendance in September and November for the fall semester and March for the spring semester. Of the members, 48 (19%) were female and six belonged to the Hispanic/Latino community. Of the members, 116 (47%) reported being U.S. Citizens or Permanent Residents and 131 (57%) listed a U.S. university as home institution. Of those institutions, 18% are located in the Midwest, 36% in the West, 29% in the Northeast, and 17% in the South. Of the members, 46% had received a Ph.D degree on or after 2000, 34% received one between 1981 and 1999, and the remaining 20% had received a Ph.D. on or prior to 1980. Detailed demographic data can be found in Section 2.

In the 2010–11 workshops, MSRI hosted 1328 separate visits (some visitors attended multiple events). Of the workshop participants, 382 (29%) were female and 777 (59%) were U.S. Citizens or Permanent Residents, of which 37 (6%) reported being a member of an underrepresented minority. In addition, 73% of the 1328 participants came from a U.S. institution. Demographic data on workshop participants can be found in Sections 2 and 4.

The Summer Graduate Schools of 2010 had 188 participants. Of those participants, 59 (31%) were female and 96 (51%) were U.S. Citizens or Permanent Residents, of which 163 (87%) students came from a U.S. institution. Demographic data on the participants of the summer graduate schools can be found in Section 4.2.

In the summer of 2011, the MSRI Undergraduate Program (MSRI-UP) hosted 18 students. Of those students, 8 (44%) were female and 18 (100%) were U.S. Citizens or Permanent Residents, of which 12 (67%) reported being a member of an under-represented minority. In addition, 18 (100%) participants came from a U.S. institution. Demographic data on MSRI-UP participants can be found in Section 5.2.

Length of Stay Summary All program members Fall 2010 Spring 2011 2010–11 2004–11 Total Member Days 8897 8476 17373 115976 Total # of Members (non-distinct) 148 126 274 1635 Average # of Days per Member 60.11 67.27 63.41 70.93 Average # of Months per Member 2.0 2.2 2.1 2.4 All female program members Fall 2010 Spring 2011 2010–11 2009–11 Total Member Days 1611 1715 3326 8192 Total # of Members (non-distinct) 29 29 58 118 Average # of Days per Member 55.55 59.14 57.34 69.42 Average # of Months per Member 1.9 2.0 1.9 2.3

1.3 Scientific Programs and their Associated Workshops

There were four major and one complementary programs for the MSRI fiscal year 2010–11, and 12 workshops were associated with them.

Note: Brief descriptions of scientific topics for each activity were reported in the Brief Report submitted in 2011. Full descriptions of each activity can be found the the Appendix Section of this Annual Report. In the lists of organizers of each activity below, an asterisk (*) denotes lead organizer(s).

Program 1: Random Matrix Theory, Interacting Particle Systems and Integrable Systems (RMT) August 16, 2010 to December 17, 2010 Organized by Jinho Baik (University of Michigan), Alexei Borodin (California Institute of Technology), Percy A. Deift* (New York University, Courant Institute), Alice Guionnet (École Normale Supérieure de Lyon, France), Craig A. Tracy (University of California, Davis), and Pierre van Moerbeke, (Université Catholique de Louvain, Belgium)

Workshop 1: Random Matrix Theory and Its Applications I September 13, 2010 to September 17, 2010 Organized by Jinho Baik (University of Michigan), Percy Deift (Courant Institute of Mathematical Sciences), Alexander Its* (Indiana University-Purdue University Indianapolis), Kenneth McLaughlin (University of Arizona), and Craig A. Tracy (University of California, Davis)

Workshop 2: Connections for Women: An Introduction to Random Matrices September 20, 2010 to September 21, 2010 Organized by Estelle Basor (American Institute of Mathematics, Palo Alto), Alice Guionnet* (Ecole Normale Supérieure de Lyon), and Irina Nenciu (University of Illinois at Chicago)

Workshop 3: Random Matrix Theory and Its Applications II December 6, 2010 to December 10, 2010 Organized by Alexei Borodin* (California Institute of Technology), Percy Deift (Courant Institute of Mathematical Sciences), Alice Guionnet (Ecole Normale Supérieure de Lyon), Pierre van Moerbeke (Universite Catholique de Louvain and Brandeis University), and Craig A.Tracy (University of California, Davis)

Program 2: Inverse Problems and Applications (IPA) August 16, 2010 to December 17, 2010 Organized by Liliana Borcea (Rice University), Maarten V. de Hoop (Purdue University), Carlos E. Kenig (University of Chicago), Peter Kuchment (Texas A&M University), Lassi Päivärinta (University of Helsinki, Finland), Gunther Uhlmann* (University of Washington), and Maciej Zworski (University of California, Berkeley)

Workshop 1: Connections for Women: Inverse Problems and Applications August 19, 2010 to August 20, 2010

Organized by Tanya Christiansen (University of Missouri, Columbia), Alison Malcolm (Massachusetts Institute of Technology), Shari Moskow (Drexel University), Chrysoula Tsogka (University of Crete), and Gunther Uhlmann* (University of Washington)

Workshop 2: Introductory Workshop on Inverse Problems and Applications August 23, 2010 to August 27, 2010 Organized by Margaret Cheney (Rensselaer Polytechnic Institute), Gunther Uhlmann* (University of Washington), Michael Vogelius (Rutgers), and Maciej Zworski (University of California, Berkeley)

Workshop 3: Inverse Problems: Theory and Applications November 8, 2010 to November 12, 2010 Organized by Liliana Borcea (Rice University), Carlos Kenig (University of Chicago), Maarten de Hoop (Purdue University), Peter Kuchment (Texas A&M University), Lassi Paivarinta (University of Helsinki), and Gunther Uhlmann* (University of Washington)

Program 3: Free Boundary Problems, Theory and Applications (FBP) January 10, 2011 to May 20, 2011 Organized by Luis Caffarelli (University of Texas, Austin), Henri Berestycki (Centre d'Analyse et de Mathématique Sociales, France), Laurence C. Evans (University of California, Berkeley), Mikhail Feldman (University of Wisconsin, Madison), John Ockendon (University of Oxford, United Kingdom), Arshak Petrosyan (Purdue University), Henrik Shahgholian* (The Royal Institute of Technology, Sweden), Tatiana Toro (University of Washington), and Nina Uraltseva (Steklov Mathematical Institute, Russia)

Workshop 1: Connections for Women: Free Boundary Problems, Theory and Applications January 13, 2011 to January 14, 2011 Organized by Catherine Bandle (University of Basel), Claudia Lederman (University of Buenos Aires), and Noemi Wolanski (University of Buenos Aires)

Workshop 2: Introductory Workshop: Free Boundary Problems, Theory and Applications January 18, 2011 to January 21, 2011 Organized by Tatiana Toro* (University of Washington)

Workshop 3: Free Boundary Problems, Theory and Applications March 7, 2011 to March 11, 2011 Organized by John King (University of Nottingham), Arshak Petrosyan (Purdue University), Henrik Shahgholian* (Royal Institute of Technology), and Georg Weiss (University of Dusseldorf)

Program 4: Arithmetic Statistics (AS) January 10, 2011 to May 20, 2011 Organized by Brian Conrey (American Institute of Mathematics), John Cremona (University of Warwick, United Kingdom), Barry Mazur (Harvard University), Michael Rubinstein* (University of Waterloo, Canada), Peter Sarnak (Princeton University), Nina Snaith (University of Bristol, United Kingdom), and William Stein (University of Washington)

Workshop 1: Connections for Women: Arithmetic Statistics

January 27, 2011 to January 28, 2011 Organized by Chantal David (Concordia University) and Nina Snaith* (University of Bristol)

Workshop 2: Introductory Workshop: Arithmetic Statistics January 31, 2011 to February 4, 2011 Organized by Barry Mazur (Harvard University), Carl Pomerance (Dartmouth College), and Michael Rubinstein* (University of Waterloo)

Workshop 3: Arithmetic Statistics April 11, 2011 to April 15, 2011 Organized by Brian Conrey (American Institute of Mathematics), Barry Mazur (Harvard University), and Michael Rubinstein* (University of Waterloo)

Program 5: Complementary Program August 16, 2010 to May 20, 2011

MSRI had a small Complementary Program comprised of one postdoctoral fellow, Jacob White from Arizona State University, a Field Medalist, Jean Bourgain from Institute for Advanced Study, and three research members, Brigitte Servatius from Worcester Polytechnic, Fatemeh Mohammadi from Ferdowsi University of Mashhad, and Wolkmar Welker from Hans- Meerweinstrasse of Marburg, Germany.

1.4 Scientific Activities Directed at Underrepresented Groups in Mathematics Each year, MSRI holds workshops on topics related to mathematical education activities. These workshops are funded by a variety of private funds as well as the supplemental grant to the NSF Five Year Grant. All MSRI activies are listed below but only the ones funded by the supplemental grant have reports in Section 11 - Appendix.

Connections for Women Workshops During the 2010–11 academic year, MSRI hosted 4 Connections for Women workhops, one for each scientific program. The goal of these workshops was to facilitate networks among women and members of underrepresented minorities. For more information regarding each workshop, please refer to Section 1.3 above.

Math Institutes Modern Math Workshop (SACNAS) Location: Anaheim, California September 29, 2010 to September 30, 2010 Organized by Ive Rubio (University of Puerto Rico at Rio Piedras), Herbert Medina (Loyola Marymount University), Chehrzad Shakiban (University of Saint Thomas), Mariel Vazquez (San Francisco State University), and Christian Ratsch (Associate Director of IPAM)

MSRI-UP 2011: Undergraduate Program June 11, 2011 to July 24, 2011 Organized by Duane Cooper (Morehouse College), Ricardo Cortez (Tulane University), Herbert Medina (Loyola Marymount University), Ivelisse Rubio (University of Puerto Rico, Rio Piedras Campus), and Suzanne Weekes* (Worcester Polytechnic Institute)

1.5 Summer Graduate Schools (Summer 2010)

SGS 1: Summer School on Operator Algebras and Noncommutative Geometry Location: University of Victoria - Victoria, BC, Canada June 14, 2010 to June 25, 2010 Organized by Heath Emerson, (University of Victoria) Thierry Giordano, (University of Ottawa) Marcelo Laca*, (University of Victoria), and Ian Putnam (University of Victoria)

SGS 2: Sage Days 22: Elliptic Curves June 21, 2010 to July 2, 2010 Organized by William Stein (University of Washington)

SGS 3: Probability Workshop: 2010 PIMS Summer School in Probability Location: University of Washington and Microsoft Research – Seattle, Washington June 21, 2010 to July 10, 2010 Organized by Krzysztof Burdzy (University of Washington), Zhenqing Chen (University of Washington), Christopher Hoffman (University of Washington), Soumik Pal (University of Washington), and Yuval Peres (University of California, Berkeley)

SGS 4: IAS/PCMI Research Summer School 2010: Image Processing Location: Park City, Utah June 27, 2010 to July 17, 2010 Organized by Tony Chan (University of California, Los Angeles), Ron Devore (University of South Carolina, Columbia), Stanley Osher (University of California, Los Angeles), and Hongkai Zhao (University of California, Irvine)

SGS 5: Mathematics of Climate Change Location: NCAR, Boulder, Colorado July 12, 2010 to July 23, 2010 Organized By Chris Jones (University of North Carolina and University of Warwick), Doug Nychka (National Center for Atmospheric Research), and Mary Lou Zeeman (Bowdoin College)

SGS 6: Algebraic, Geometric, and Combinatorial Methods for Optimization August 2, 2010 to August 13, 2010 Organized by Matthias Köppe (University of California, Davis) and Jiawang Nie (University of California, San Diego)

1.6 Other Scientific Workshops

Workshop 1: 21st Bay Area Discrete Math Day October 16, 2010 Organized by Federico Ardila (San Francisco State University), Ruchira Datta (University of California, Berkeley), Tim Hsu (San Jose State University), Fu Liu (University of California, Davis), Carol Meyers (Lawrence Livermore National Laboratory), Raman Sanyal* (University of California, Berkeley), Rick Scott (Santa Clara University), and Ellen Veomett (California State University, East Bay)

Workshop 2: Bay Area Differential Geometry Seminar (BADGS) 2010-11 10

October 23, 2010, February 05, 2011 and April 23, 2011 Organized by David Bao (San Francisco State University), Robert Bryant (Mathematical Sciences Research Institute), Joel Hass (University of California, Davis), David Hoffman* (Stanford University), Rafe Mazzeo (Stanford University), and Richard Montgomery (University of California, Santa Cruz)

Workshop 3: Hot Topics: Kervaire Invariant October 25, 2010 to October 29, 2010 Organized by Mike Hill (University of Virginia), Michael Hopkins (Harvard University), and Douglas C. Ravanel* (University of Rochester)

Workshop 4: SIAM/MSRI Workshop on Hybrid Methodologies for Symbolic-Numeric Computation November 17, 2010 to November 19, 2010 Organized by Mark Giesbrecht (University of Waterloo), Erich Kaltofen* (North Carolina State University), Daniel Lichtblau (Wolfram Research), Seth Sullivant (North Carolina State University), and Lihong Zhi (Chinese Academy of Sciences, Beijing)

1.7 Educational & Outreach Activities Each year, MSRI holds workshops on topics related to mathematical education activities. These workshops are funded by a variety of private funds as well as the supplemental grant to the NSF Five Year Grant. All MSRI activies are listed below but only the ones funded by the supplemental grant have reports in Section 11 - Appendix.

Workshop 1: Summer Institute for the Professional Development of Middle School Teachers (Wu Summer 2010 Institute) July 6, 2010 to July 23, 2010 Organized by Hung-Hsi Wu (University of California, Berkeley)

Workshop 2: Workshop on Mathematics Journals February 14, 2011 to February 16, 2011 Organized by James M Crowley (Society for Industrial and Applied Mathematics), Susan Hezlet* (London Mathematical Society), Robion C Kirby (University of California, Berkeley), and Donald E McClure (American Mathematical Society)

Workshop 3: Bay Area Circle for Teachers June 21, 2010 to June 25, 2010 and January 29, 2011 Organized by Brandy Wiegers (MSRI)

Workshop 4: Circle on the Road Spring 2011 Supported by the NSF Suppl. Grant DMS-0937701 to the Core Grant DMS-0441170 (2005–10) March 18, 2011 to March 20, 2011 Organized by Dave Auckly (MSRI), Matthias Kawski (Arizona State University), Jeff Morgan (University of Houston), Mark Saul (Bronx High School, retired), and Sam Vandervelde (Saint Lawrence University)

Workshop 5: Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers

Supported by the NSF Suppl. Grant DMS-0937701 to the Core Grant DMS-0441170 (2005–10) May 11, 2011 to May 13, 2011 Organized by Dave Auckly (MSRI), Sybilla Beckmann* (University of Georgia), Jim Lewis (University of Nebraska Lincoln) and William McCallum (University of Arizona)

1.8 Programs Consultant List

Consultant Disciplinary Consultant Name(s) Specialty Consultant Employer Activity Title David Bao Differential geometry San Francisco State University Differential geometry seminar Mathias Beck Discrete geometry San Francisco State University Bay Area Circle for Teachers Climate Change: Summer School & Economic Games and Mechanisms to Address Climate Inez Fung Climate change University of California, Berkeley Change Philip Griffith Algebraic geometry Institute for Advanced Study Future program Susan Hezlet London Math. Society Workshop on Mathematics Journals University of North Carolina at Chris Jones Climate change Chapel Hill Climate change: Summer School Moris Kalka Differential geometry Tulane University Summer Graduate Workshops Rob Kirby Topology University of California, Berkeley Open Access Journals Jacob Lurie Algebraic topology Harvard University Future program William Macallum Education University of Arizona Educational workshops Rafe Mazzeo Differential geometry Stanford University Differential geometry seminar Donald McClure Image processing Brown University AMS Open Access Curt McMullen Geometric Topology Harvard University Future program Robert Megginson Fuctional Analysis University of Michigan Diversity Recruitment Computational Lawrence Berkeley National Juan Meza mathematics Laboratory MSRI - UP Richard Montgomery Differential geometry University of California, Santa Cruz Differential geometry seminar Assaf Naor Probability New York University Quantative Geometry Climate Change: Summer School & Economic National Center for Atmospheric Games and Mechanisms to Address Climate Douglas Nychka Climate change Research Change Jim Pitman Statistics MassachussettsUniversity of California, Institute Berkeley of Vmath Bjorn Poonen Model theory Technology Future program Igor Rodnianski Hyperbolic PDE MIT Hot Topics: Black Holes in Relativity Perter Sarnak Number theory University of Princeton Future program Mark Saul Education Education Development Center Great Circles Tatiana Shubin Number theory San Jose State University Bay Area Circle for Teachers Ted Slaman Logic University of California, Berkeley Future program Zvesda Stankova Algebraic geometry Mill College Math Circles Sam Vandervelde Number theory St. Lawrence University Math Circles Math. Professional Dev. Instiute (Wu Summer Hung-Hsi Wu Differential geometry University of California, Berkeley Institute) Mary Lou Zeeman Climate change Bowdoin College Toric Varieties David Zetland Climate change University of California, Berkeley Climate Change: Summer School Educational Advisory UsingTeaching Partnerships Undergraduates to Strengthen Mathematics Elementary Committee (EAC) See Section 10: Committee Membership Mathematics Teacher Education Human Resources PromotingMath Institutes Diversity Modern at theMathematics Graduate LevelWorkshop in Advisory Committee Mathematics: a National Forum (HRAC) See Section 10: Committee Membership MSRI - UP Random Matrix Theory Inverse Problems and Applications Scientific Advisory Free Boundary Problems Committee (SAC) & Arithmetic Statistics HRAC See Section 10: Committee Membership Complementary Program

2. Program and Workshop Data

2.1 Program Participant List (See e-mail attached file)

2.2 Program Participant Summary

# of US Citizens Home # of & Perm. # of # of Instituti Programs Members Res. % Female % Minorities1 % on % Random Matrix Theory, Interacting Particle Systems and Integrable Systems 50 21 42.0% 8 16.0% 0 0.0% 25 50.0% Inverse Problems and Applications 76 34 44.7% 14 18.4% 1 4.3% 42 55.3% Free Boundary Problems, Theory and Applications 51 18 35.3% 15 29.4% 3 20.0% 23 45.1% Arithmetic Statistics 64 39 60.9% 9 14.1% 0 0.0% 37 57.8% Complementary Program 2010-11 6 4 66.7% 2 33.3% 0 0.0% 4 66.7%

Total # of Distinct Members 247 116 47.0% 48 19.4% 4 4.2% 131 53.0% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

2.3 Program Members Demographic Data 2010–11 Program Members Demographic Summary

% (No Gender # Decl.)* % # of Distinct Members 247 100.0% 19% Male 199 80.57% 80.6% Female 48 19.43% 19.4% Male Decline to State Gender 0 0.0% 81% Female

% (No Native American Ethnicities # Decl.)* %

Native American 0 0.00% 0.0% Asian Asian 19 12.34% 7.7% Black 1 0.65% 0.4% Black Hispanic 6 3.90% 2.4% 51.4% Hispanic Pacific 1 0.65% 0.4% 34.4% White 127 82.47% 51.4% Pacific Decline to State Ethnicities 85 34.4% Unavailable Information 7 2.8% White 0.4% 0.4% 0.0% 2.8% Decline to State Minorities 4 4.2% 2.4% Ethnicities Unavailable 7.7% Information

Citizenships # % US Citizen & Perm. Residents 116 47.0% Foreign 131 53.0% Unavailable information 0 0.0% # of Distinct Members 247 100.0% 47% Home Inst. in 53% US US Citizen 95 38.5% Perm Residents 21 8.5% Home Inst. NOT in US Home Inst. in US 131 53.04%

Year of Ph.D # % 2011 & Later 4 1.6% 2010 16 6.5% 2005-2009 63 25.5% 2% 2011 & Later 6% 2000-2004 29 11.7% 2010 1995-1999 29 11.7% 20% 2005-2009 1990-1994 20 8.1% 6% 26% 2000-2004 1985-1989 21 8.5% 8% 1995-1999 1981-1984 15 6.1% 8% 12% 1980 & Earlier 50 20.2% 12% 1990-1994 Unavailable Info. 0 0.0% 1985-1989 Total # of Distinct Members 247 100.0% 1981-1984 *Statistic Calculation based on all participants that did not decline. 1980 & Earlier

Programs Random Matrix Theory, Interacting Particle Systems and Integrable Systems Inverse Problems and Applications Free Boundary Problems, Theory and Applications Arithmetic Statistics Complementary Program 2010-11

2010–11 Program Members Home Institution Classified by States *Regions based on US Census classification

2007 Census State #% Population South 22 16.8% 36.6% AL - 0.0% 1.5% AR - 0.0% 0.9% DE 2 1.5% 0.3% DC 1 0.8% 0.2% South Northeast FL - 0.0% 6.1% 17% GA 1 0.8% 3.2% 29% KY 2 1.5% 1.4% West LA - 0.0% 1.4% Midwest MD 2 1.5% 1.9% 18% 36% MS - 0.0% 1.0% NC - 0.0% 3.0% OK - 0.0% 1.2% SC - 0.0% 1.5% TN 1 0.8% 2.0% TX 13 9.9% 7.9% VA - 0.0% 2.6% WV - 0.0% 0.6% West 47 35.9% 23.2% AK - 0.0% 0.2% AZ 4 3.1% 2.1% HI - 0.0% 0.4% ID - 0.0% 0.5% MT - 0.0% 0.3% CA 30 22.9% 12.1% CO 1 0.8% 1.6% NV - 0.0% 0.9% NM - 0.0% 0.7% OR 1 0.8% 1.2% UT 3 2.3% 0.9% WA 8 6.1% 2.1% WY - 0.0% 0.2% Midwest 24 18.3% 22.0% IL 2 1.5% 4.3% IN 9 6.9% 2.1% IA 1 0.8% 1.0% KS 1 0.8% 0.9% MI 6 4.6% 3.3% MN 1 0.8% 1.7% MO - 0.0% 1.9% ND - 0.0% 0.2% NE - 0.0% 0.6% OH 2 1.5% 3.8% SD - 0.0% 0.3% WI 2 1.5% 1.9% Northeast 38 29.0% 18.1% CT 1 0.8% 1.2% ME 1 0.8% 0.4% MA 12 9.2% 2.1% NH 2 1.5% 0.4% NJ 6 4.6% 2.9% NY 10 7.6% 6.4% PA 6 4.6% 4.1% RI - 0.0% 0.4% VT - 0.0% 0.2% Other - 0.0% 0% PR - 0.0% 0% Other - 0.0% 0% Total 131 100% 100% 15

2010–11 Program Members Home Institution Classified by Countries *Regions based on United Nations classification

Americas 145 North America Canada 11 Americas United States 131 South America Argentina 2 59% Uruguay 1 Asia Asia 9 3% East Asia China 1 Japan 2 Europe 37% South-central Asia India 2 Iran 1 Oceania Western Asia Israel 2 1% Turkey 1 Europe 91 Eastern Europe Russia 3 Ukraine 1 Northern Europe England 21 Finland 11 Norway 1 Sweden 11 Southern Europe Greece 1 Italy 3 Spain 6 Western Europe Austria 1 Belgium 6 France 13 Germany 10 Netherlands 2 Switzerland 1 Oceania 2 Australia & NZ Australia 2 Grand Total 247

2.4 Workshop Participant List (See e-mail attached file)

2.5 Workshop Participant Summary

# of US Citizens Home # of & Perm. # of # of Instituti Workshops Participants Res. % Female % Minorities1 % on % 16 Scientific Workshops Arithmetic Statistics Research 79 43 54.4% 15 19.0% 1 3.0% 48 60.8% Connections for Women: An Introduction to Random Matrices 51 11 21.6% 31 60.8% 0 0.0% 20 39.2% Connections for Women: Arithmetic Statistics 38 25 65.8% 22 57.9% 0 0.0% 29 76.3% Connections for Women: Free Boundary Problems, Theory and Applications 30 4 13.3% 21 70.0% 0 0.0% 19 63.3% Connections for Women: Inverse Problems and Applications 47 23 48.9% 28 59.6% 3 15.8% 38 80.9% Free Boundary Problems, Theory and Applications Research 67 24 35.8% 15 22.4% 2 13.3% 40 59.7% Introductory Workshop on Inverse Problems and Applications 99 46 46.5% 30 30.3% 3 8.6% 74 74.7% Introductory Workshop: Arithmetic Statistics 82 60 73.2% 19 23.2% 2 3.6% 67 81.7% Introductory Workshop: Free Boundary Problems, Theory and Applications 41 13 31.7% 13 31.7% 1 10.0% 30 73.2% Inverse Problems: Theory and Applications Research 118 58 49.2% 25 21.2% 5 10.2% 81 68.6% Random Matrix Theory and Its Applications I 129 55 42.6% 31 24.0% 1 2.1% 76 58.9% Random Matrix Theory and its Applications II 107 51 47.7% 15 14.0% 1 2.4% 75 70.1% 21st Bay Area Discrete Math Day (BADMath Day) 81 72 88.9% 18 22.2% 2 2.9% 75 92.6% Bay Area Differential Geometry (BADG) Seminar Fall 2010 21 16 76.2% 1 4.8% 0 0.0% 18 85.7% Hot Topics: Kervaire invariant 41 28 68.3% 10 24.4% 0 0.0% 32 78.0% SIAM/MSRI workshop on Hybrid Methodologies for Symbolic-Numeric Computation 50 28 56.0% 7 14.0% 0 0.0% 30 60.0% All 19 Workshops Total 1,081 557 51.5% 301 27.8% 21 4.4% 752 69.6%

3 Education & Outreach Workshops Circle on the Road Spring 2011 82 73 89.0% 25 30.5% 4 5.7% 75 91.5% Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers 104 101 97.1% 44 42.3% 12 12.6% 101 97.1% Workshop on Mathematics Journals 61 46 75.4% 12 19.7% 0 0.0% 48 78.7% All 19 Workshops Total 247 220 89.1% 81 32.8% 16 7.8% 224 90.7%

All 19 Workshops Total 1,328 777 58.5% 382 28.8% 37 5.5% 976 73.5% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

2.6 Workshop Participant Demographic Data 2010–11 Workshop Participants Demographic Summary

% (No Decl.)* % Gender # Male # of Participants 1328 100.0% 68% Male 898 70.16% 67.6% Female Female 382 29.84% 28.8% Decline to State Gender 48 3.6% 29% Decline to State 3% Gender

% (No Ethnicities # Decl.)* % Native American Native American 3 0.26% 0.2% Asian Asian 249 21.65% 18.8% Black 16 1.39% 1.2% Black Hispanic 63 5.48% 4.7% 61.3% Pacific 5 0.43% 0.4% Hispanic White 814 70.78% 61.3% 17.2% 18.8% Pacific Decline to State Ethnicities 228 17.2% Unavailable Information 0 0.0% White 0.4% 0.0% Minorities 37 5.5% Decline to State 4.7% 0.2% Ethnicities 1.2% Unavailable Information Citizenships # % US Citizen & Perm. Residents 777 58.5% Foreign 545 41.0% Unavailable information 6 0.5% # of Particpants 1328 100.0% 27% Home Inst. in US

US Citizen 678 51.1% 73% Home Inst. NOT Perm Residents 99 7.5% in US

Home Inst. in US 976 73.49%

Year of Highest Degree # % 2011 & Later 35 2.6% 2010 105 7.9% 2011 & Later 2010 2005-2009 518 39.0% 11% 2000-2004 146 11.0% 39% 2005-2009 1995-1999 114 8.6% 8% 2000-2004 1990-1994 77 5.8% 1995-1999 1985-1989 75 5.6% 1990-1994 13% 6% 1981-1984 75 5.6% 1985-1989 1980 & Earlier 173 13.0% 8% 6% 1981-1984 Unavailable Info. 10 0.8% 2% 1% 6% 1980 & Earlier Total # Participants 1328 100.0% Unavailable Info. *Statistic Calculation based on all participants that did not decline.

2010–11 Workshops Arithmetic Statistics Research Connections for Women: An Introduction to Random Matrices Connections for Women: Arithmetic Statistics Connections for Women: Free Boundary Problems, Theory and Applications Connections for Women: Inverse Problems and Applications Free Boundary Problems, Theory and Applications Research Introductory Workshop on Inverse Problems and Applications Introductory Workshop: Arithmetic Statistics Introductory Workshop: Free Boundary Problems, Theory and Applications Inverse Problems: Theory and Applications Research Random Matrix Theory and Its Applications I Random Matrix Theory and its Applications II 21st Bay Area Discrete Math Day (BADMath Day) Bay Area Differential Geometry (BADG) Seminar Fall 2010 Hot Topics: Kervaire invariant SIAM/MSRI workshop on Hybrid Methodologies for Symbolic-Numeric Computation Circle on the Road Spring 2011 Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers Workshop on Mathematics Journals 18

2010–11 Workshop Participants Home Institution Classified by States *Regions based on US Census classification 2007 Census State #% Population South 146 15.0% 36.6% AL 5 0.5% 1.5% AR - 0.0% 0.9% DE 8 0.8% 0.3% DC 3 0.3% 0.2% FL 4 0.4% 6.1% 46% GA 12 1.2% 3.2% 15% KY 2 0.2% 1.4% 12% 9% LA 3 0.3% 1.4% 18% MD 10 1.0% 1.9% MS 1 0.1% 1.0% South West NC 15 1.5% 3.0% Midwest Northeast OK 1 0.1% 1.2% Other SC 3 0.3% 1.5% TN 1 0.1% 2.0% TX 66 6.8% 7.9% VA 12 1.2% 2.6% WV - 0.0% 0.6% West 454 46.5% 23.2% AK 1 0.1% 0.2% AZ 18 1.8% 2.1% HI - 0.0% 0.4% ID - 0.0% 0.5% MT - 0.0% 0.3% CA 348 35.7% 12.1% CO 13 1.3% 1.6% NV 1 0.1% 0.9% NM 1 0.1% 0.7% OR 12 1.2% 1.2% UT 10 1.0% 0.9% WA 49 5.0% 2.1% WY 1 0.1% 0.2% Midwest 118 12.1% 22.0% IL 34 3.5% 4.3% IN 30 3.1% 2.1% IA 5 0.5% 1.0% KS 2 0.2% 0.9% MI 22 2.3% 3.3% MN 6 0.6% 1.7% MO 2 0.2% 1.9% ND - 0.0% 0.2% NE 4 0.4% 0.6% OH 4 0.4% 3.8% SD - 0.0% 0.3% WI 9 0.9% 1.9% Northeast 174 17.8% 18.1% CT 5 0.5% 1.2% ME 2 0.2% 0.4% MA 42 4.3% 2.1% NH 9 0.9% 0.4% NJ 21 2.2% 2.9% NY 58 5.9% 6.4% PA 22 2.3% 4.1% RI 12 1.2% 0.4% VT 3 0.3% 0.2% Other 84 8.6% 0% PR - 0.0% 0% Unavailable 84 8.6% 0% Total 976 100% 100% 19

2010–11 Workshop Participants Home Institution Classified by Countries *Regions based on United Nations classification

Africa 1 Western Africa Nigeria 1 Americas 1036 Central America Mexico 4 North America Canada 42 United States 976 South America Argentina 3 Brazil 7

Chile 2 Uruguay 2 Asia 43 East Asia China 2 Japan 11 Korea, Republic of 11 78% Taiwan 1 South-central Asia India 6 Iran 6 South-eastern Asia Philippines 3 Western Asia Israel 2 Saudi Arabia 1 18% Europe 230 Eastern Europe Polan 2 0% Romania 2 3% Russia 7 1% 0% Ukraine 8 Northern Europe England 41 Finland 20 Africa Iceland 1 Norway 2 Americas Scotland 8 Asia Sweden 19 Southern Europe Albania 1 Europe Greece 2 Italy 10 Oceania Portugal 2 Spain 15 Unavailable information Western Europe Austria 2 Belgium 15 France 40 Germany 22 Netherlands 6 Switzerland 5 Oceania 3 Australia & NZ Australia 3 Unavailable information 15 Grand Total 1328

2.7 Program Publication List

In summary, 13 papers have been accepted or appeared, another 25 papers have been posted on arXiv and 65 manuscripts have been submitted to various journals.

Last Name First Name Publication Title Co-author(s) Status Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix Bender Martin ensembles Gernot Akemann accepted/appeared Caustics, counting maps and semi- Ercolani Nicholas classical asymptotics accepted/appeared Approximation by polynomials and Blaschke products having all zeros Farmer David on a circle Pamela Gorkin accepted/appeared "Comparison principles for self- Feldman Mikhail similar potential flow" Gui-Qiang Chen accepted/appeared "Transonic Shocks In Multidimensional Divergent Feldman Mikhail Nozzles" Myoungjean Bae accepted/appeared The limiting Kac random polynomial and truncated random Forrester Peter orthogonal polynomials accepted/appeared Double scaling limit for modified Kuijlaars Arnoldus Jacobi-Angelesco polynomials Klaas Deschout accepted/appeared Arrival times for the Wave McLaughlin Joyce Equation Jeong-Rock Yoon accepted/appeared Two-dimensional shear wave Kui Lin, Ashley speed and crawling wave speed Thomas, Kevin Parker, recoveries from in vitro prostate Ben Castaneda, McLaughlin Joyce data Deborah Rubens accepted/appeared Multiplicative properties of sets of Pomerance Carl residues Andrzej Schinzel accepted/appeared Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Nils-Peter Skoruppa, Ryan Nathan Two Fredrik Stromberg accepted/appeared The 1 1-dimensional Kardar-Parisi- Zhang equation and its universality Spohn Herbert class Tomohiro Sasmoto accepted/appeared Nonlinear porous medium flow Vazquez Juan with fractional potential pressure Luis Caffarelli accepted/appeared Non-intersecting random walks in the neighborhood of a symmetric P.van Moerbeke and P. Adler Mark tacnode Ferrari posted Consecutive Minors for Dyson's P.van Moerbeke and E. Adler Mark Brownian Motions Nordenstam posted Topological expansion in the cubic Bleher Pavel random matrix mode Alfredo Deano posted

Multiple change-point Poisson model for threshold exceedances of Janos Gyarmati-Szabo, Bogachev Leonid air pollution concentrations Haibo Chen posted

Classification of radial solutions to the Emden-Fowler equation on the F. Gazzola, G. Grillo, Bonforte Matteo hyperbolic space J. L. Vazquez posted Lattice Index Jacobi Forms over Boylan Hatice Number Fields Nils Peter Skoruppa posted Linear Characters of SL_2 over Boylan Hatice Dedekind Domains Nils Peter Skoruppa posted On the Computation of Jacobi Nils Peter Skoruppa Boylan Hatice Forms over Number Fields and Shuichi Hayashida posted Topological expansion in the cubic Deao Alfredo random matrix model Pavel M. Bleher posted Sally Koutsoliotas and Farmer David Maass forms on GL(3) and GL(4) Stefan Lemurell posted Hezari Hamid spectral rigidity of an ellipse Steve Zelditch posted Relative p-adic Hodge theory, I: Kedlaya Kiran Foundations Ruochuan Liu posted Relative p-adic Hodge theory, II: Kedlaya Kiran (phi, Gamma)-modules Ruochuan Liu posted 2D and 3D reconstructions in Kuchment Peter acousto-electric tomography L. Kunyansky posted Sparsity promoting bayesian Kolehmainen, Lassas, Lassas Matti inversion Niinimski, Siltanen posted The beta-Hermite and beta- Li Luen-Chau Laguerre processes posted Primality testing with Gaussian Pomerance Carl periods Hendrik Lenstra posted Families of Quasimodular Forms and Jacobi Forms: Partition Rhoades Robert Statistics posted False, Partial, and Mock Jacobi Theta Functions as q- K. Bringmann and A. Rhoades Robert hypergeometric Series Folsom posted All the lowest order PDE for Rumanov Igor spectral gaps of Gaussian matrices posted

A generalized plasma and interpolation between classical Sinclair Christopher random matrix ensembles Peter J Forrester posted Skoruppa Nils-Peter Jacobi forms over number fields Hatice Boylan posted Martin Raum, Nathan Ryan, Gonzalo Skoruppa Nils-Peter Formal Siegel modular forms Tornario posted The one-dimensional KPZ equation with initial sharp wedge Spohn Herbert and the Airy process Sylvain Prolhac posted 22

Stein William What is Riemann's Hypothesis Barry Mazur posted Regularity for the no-sign Obstacle E. Lindgren, H Andersson John problem Shahgholian submitted Optical Tomography in weakly scattering media in presence of Arridge Simon strong scatterers V. Soloviev submitted Difuse Optical Cortical Mapping Arridge Simon with Boundary Element method J Elisee submitted Burkholder integrals, Morrey's Tadeusz Iwaniec, problem and quasiconformal Istvan Prause, Eero Astala Kari mappings. Saksman submitted

Modelling threshold exceedances of air pollution concentrations via non-homogeneous Poisson process Janos Gyarmati-Szabo, Bogachev Leonid with multiple change-points Haibo Chen submitted Waveform-Diverse Moving-Target Cheney Margaret Spotlight Synthetic-Aperture Radar Brett Borden submitted Vanishing and nonvanishing theta Cohen Henri values Don Zagier submitted Holder estimates for competing Kelei wang and Zhitao Dancer Edward species equations Zhang submitted scattering enabled retrieval of Green's functions from remotely incident wave packets using cross de Hoop Maarten correlations J. Garnier, K. Solna submitted Partial Cauchy Data for General Secon-Order Elliptic Operators in M. Yamamoto, G. Emanouilov (Imanuvilov) Oleg two dimensions Uhlmann submitted

Global uniqueness in determining a coefficient of two dimensional Schrodinger equation by boundary M. Yamamoto, G. Emanouilov (Imanuvilov) Oleg data on disjoint subboundaries Uhlmann submitted Determination of second -order elliptic operators in two dimensions from partial Cauchy M. Yamamoto, G. Emanouilov (Imanuvilov) Oleg data Uhlmann submitted

Aleksandrov-Bakelman-Pucci type estimates for integro-differential Guillen Nestor equations Russell Schwab submitted Regularity for non-local almost minimal boundaries and Guillen Nestor applications Cristina Caputo submitted Schur Function expansions of KP tau functions associated to Harnad John algebraic curves V. Enolski submitted spectral uniqueness of radial Kiril Datchev, Ivan Hezari Hamid schrodinger operators Ventura submitted

A Random Matrix Model for Eduardo Duenez, Jon Elliptic Curve L-Functions of Keating, Steven J Huynh Duc Khiem Finite Conductor Miller, Nina Snaith submitted The eigenvalue problem of singular Hynd Ryan ergodic control submitted Critical Zeros of Dirichlet L- Brain Conrey and Iwaniec Henryk functions Kannan Soundararajan submitted Brian Conrey and Iwaniec Henryk Asymptotic Large Sieve Kannan Soundararajan submitted A concentration inequality for the Kargin Vladislav sum of two random matrices submitted

A compact hamiltonian with the same mean spectral density as the Keating Jon Riemann zeros Sir Michael Berry submitted The support theorem for the single Kuchment Peter radius spherical mean transform M. Agranovsky submitted The Hermitian two matrix model Maurice Duits and Man Kuijlaars Arnoldus with an even quartic potential. Yue Mo submitted

Non-intersecting squared Bessel Andrei Martinez paths: critical time and double Finkelshtein and Kuijlaars Arnoldus scaling limit. Franck Wielonsky submitted Critical behavior of non- intersecting Brownian motions at a Steven Delvaux and Kuijlaars Arnoldus tacnode. Lun Zhang submitted Counting smooth solutions to the Lagarias Jeffrey equation A B=C K. Soundararajan submitted

New Energy Inequalities For Tensorial Wave Equations On A. Burtscher, J.D.E LeFloch Philippe One-Sided Bounded Spacetim Grant submitted Optimal regularity for the no-sign John Andersson, Lindgren Erik obstacle problem Henrik Shahgholian submitted Stability for the Infinity-Laplace Lindgren Erik Equation with variable exponent Peter Lindqvist submitted A note on the regularity of the inhomogeneous infinity laplace Lindgren Erik equation submitted An Analysis of Electrical Impedance Tomography with Applications to Tikhonov Maass Peter Regularization Bangti Jin submitted Optimal Source for Maximum Distinguishability in Optical Taufiquar Khan, Bangti Maass Peter Imaging Jin, Bonnie Jacob submitted Asymptotic expansions for crank K. Bringmann and R. Mahlburg Karl and rank moments Rhoades submitted

Convolution bootstrap percolation models, Markov-type processes, K. Bringmann and A. Mahlburg Karl and mock theta functions Mellit submitted Coefficient formulas for traces of Mahlburg Karl affine Lie superalgebras K. Bringmann submitted Improving Arrival Time Identification in Transcient Jens Klein, Daniel McLaughlin Joyce elastography Renzi submitted A linear hyperbolic scheme to recover frequency dependent Kui Lin, Ashley complex shear moduli in thomas, C. Hazard, K. viscoelastic models utilizing one or Thomenius, J. Hah, K. McLaughlin Joyce more displacement data sets Parker and D. Rubens submitted Verifying the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank zero Miller Robert and one None specified submitted Explicit Isogeny descent on elliptic Miller Robert curves Michael Stoll submitted

Exterior Cloaking with active Fernando Guevara sources in two dimensional Vasquez and Daniel Milton Graeme acoustics Onofrei submitted On the dimension of p-harmonic John Lewis, Andrew Nystrom Kaj measure in space Vogel submitted

An inverse problem for the wave equation with one measurement Matti Lassas, Tapio Oksanen Lauri and the pseudorandom noise Helin submitted Book: Regulaity of free boundaries H. Shagholian, N. Petrosyan Arshak in obstacle type problems Uraltseva submitted A two-phase problem with lower Petrosyan Arshak dimensional free boundary M. Allen submitted

An adaptive phase space method Eric Chung, Gunther with application to reflection Uhlmann, Hongkai Qian Jianliang traveltime tomography Zhao submitted Homogenization of Maxwellâ€™s Schotland John equations in periodic composites Vadim Markel submitted Optimal regularity of no-sign John Anderssn, Erik Shahgholian Henrik obstacle problem Lindgren submitted Ville Kolehmainen, Sparsity-promoting Bayesian Matti Lassas, Kati Siltanen Samuli inversion Niinimaki submitted Kari Astala, Jennifer Direct electrical impedance Mueller, Allan tomography for nonsmooth Peramaki, Lassi Siltanen Samuli conductivities Paivarinta submitted Jacobi forms of critical and Skoruppa Nils-Peter singular weight Hatice Boylan submitted

Strichartz estimates for Dirichlet wave equations in two dimensions Chris Sogge, Chengbo Smith Hart with application Wang submitted

wo-point generating function of the free energy for a directed polymer Spohn Herbert in a random medium Sylvain Prohlac submitted

Two-point generating function of the free energy for a directed Spohn Herbert polymer in a random medium Sylvain Prolhac submitted Growing interfaces uncover universal fluctuations behind scale K. Takeuchi, M. Sano, Spohn Herbert invariance T. Sasamoto submitted A New Numerical Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Qian, Uhlmann and Stefanov Plamen Speed Zhao submitted Elliptic equations with singular BMO coeï¬ƒcients in Reifenberg Um Ko Woon domains submitted Regularity of Free Boundaries in A. Petrosyan, H. Uraltseva Nina Obstacle-Type Problems Shahgholian submitted Propagation through trapped sets and semiclassical resolvent Vasy Andrais estimates Kiril Datchev submitted Morawetz estimates for the wave Vasy Andrais equation at low frequency Jared Wunsch submitted On the homology of the real complement of the k-parabolic Helene Barcelo, White Jacob subspace arrangement Christopher Severs submitted Pentagonal Relations and the Exchange Module of the type A_n Helene Barcelo, White Jacob Cluster Algebra Christopher Severs submitted On Multivariate Chromatic Polynomials of Hypergraphs and White Jacob Hyperedge Elimination Jacob White submitted Low-lying zeros of Dedekind zeta functions attached to S_{4} quartic Yang Andrew fields submitted Domino Shuffling for the Del Pezzo Young Benjamin 3 lattice Cyndie Cottrell submitted

2.8 Program Publication Work-In-Progress List

For the work-in-progress publications, MSRI members produced 114 rough drafts and 137 notes. (See e-mail attached file)

3. Postdoctoral Program

3.1 Description of Activities

The postdoctoral program at MSRI is central to MSRI’s mission of continued excellence in mathematics research. The semester-long and year-long programs MSRI organizes and hosts produce the leading research in that field of study. MSRI’s postdocs engage with fellow mathematicians from all over the world to develop their interests and contribute to the Science community. During the 2010–11 academic year, MSRI selected 31 postdoctoral scholars with research interests in the programs that MSRI offers. Of those postdocs, 26 were funded by the NSF Core Grant, three by the NSA Grant, and two by the Viterbi Endowment.

There were many more excellent postdoc applicants than we could fund with our NSF Postdoctoral Fellowship (PD) budget line. The program organizers used additional funds from their allocated NSF budget to support an additional 15 members who had earned their PhDs no more than five years ago. Those members were called “Postdoc Research Members” (PD/RMs as opposed to NSF Postdoctoral Fellows) and received a per diem of $2,400 per month. While they were not monetarily compensated at the same level as the NSF Postdoctoral Fellows, they received all other privileges. That is, all Postdocs were assigned a mentor upon their arrival, participated in a weekly Postdoc seminar, and were a vibrant part of the research community. They also had the same logistic privileges (office, library access, bus pass, etc…).

Of the 31 Postdoctoral Fellows at MSRI, seven (23%) were female, nine (29%) were a U.S. Citizen or Permanent Resident, and 16 (52%) came from a US institution. The program organizers were extremely satisfied with the Postdoctoral program and believed that it was by all accounts an enormous success.

Here are additional details on the NSF Postdoctoral Fellows for each program.

Random Matrix Theory

Martin Bender received his Ph.D. from the KTH Royal Institute of Technology in 2008. Before joining MSRI, he worked towards his post doctorate at the Katholeike Univereiteit Leuven from 2008 to 2010. While at MSRI, Bender worked on various projects under the mentorship of Arno Kuijlaars. He created a paper titled "Multiple Meixner-Pollaczek polynomials and the six-vertex model" with Steven Delvaux and Arno Kuijlaars, which was submitted to JAP. In addition, he wrote "Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles" with co-author Gernot Bender, Martin Akemann. Bender felt that his stay at MSRI was an excellent opportunity to study with leading experts in the field.

Kargin Vladislav received his Ph.D. from the Courant Institute, NYU in 2008. Before joining MSRI, he worked towards his post doctorate at Stanford University as a Szego assistant professor. While at MSRI, he worked on various projects under the mentorship of Amir Dembo and studied ensembles of random matrices arising in free probability. In particular, Vladislav investigated local limit laws for the distribution of their eigenvalues, which was written up and submitted to a journal. Vladislav found that the main benefit of the postdoc position at MSRI was the possibility to interact with many researchers with similar interests. Specifically, the workshop, "Connections for Women," was especially Kargin, Vladislav useful for him since many of its participants have similar interests on border of free probability and random matrix theory. After joining MSRI, he continued his work at Stanford University as a Szego assistant professor. In addition, Kargin stated, “The general atmosphere at MSRI was very congenial. The staff was accessible and the library and computer facilities are excellent. I would be very glad to come again.”

Karl Liechty received his Ph.D. from Indiana University and Purdue University in Indianapolis in 2010 under the supervision of Pavel Bleher. His dissertation was titled “Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice”. While at MSRI, Liechty started a paper on "Non-intersecting random walks on an interval" with the mentorship of Pavel Bleher. He also collaborated with Pavel Bleher on a monograph on "Random matrix theory and the six-vertex model.” In addition to substantial progress they made on these projects, Liechty also

Liechty, Karl discussed several potential collaborations with fellow postdocs. It remains to be seen which of these gets off the ground, but he is optimistic that the collaborations will be fruitful. After his stay at MSRI, Karl Liechty continued as a Postdoctoral Assistant Professor for the University of Michigan. Liechty noted, “Overall, the semester was incredible for me. I probably don't even realize how much I learned over the course of the semester. There were a lot of seminars throughout the semester. The biggest difficulty for me was trying to find a balance between attending the seminars and learning new things, discussing potential collaborations, and working on existing projects.”

Eric Nordenstam received his Ph.D. from the Swedish Royal Institute of Technology for Prof. Kurt Johansson in 2009. Before joining MSRI, he worked towards his post doctorate at Université Catholique de Louvain, Louvain-La-Neuve, Belgium, working with Prof. Pierre van Moerbeke. While at MSRI, he worked on various projects under the mentorship of Pierre van Moerbeke. While at MSRI, he met Jonathan Novak and Ben Fleming, and they created and studied an interesting discrete model which will certainly lead to a publication. With Ken McLaughlin and Ben Fleming, he discussed a problem of domino tilings with a certain boundary condition and also had something of a study circle on the results of Kenyon Nordenstam, Eric and Okounkov about limit shapes in tilings. After his stay at MSRI, Nordenstram continued his postdoc working with Christian Krattenthaler and the University of Vienna. Nordenstam stated, “I would like to express my gratitude to the organizers of the program for giving me this opportunity. I should also like to thank the staff, directorate and financial benefactors of MSRI for creating this special environment and standing up for pure basic science.”

Jonathan Novak completed his Ph.D. at Queen's University in 2009. Before joining MSRI, he worked towards his post doctorate at the University of Waterloo. While at MSRI, he worked on various projects under the mentorship of Amir Dembo. He completed writing "What is... a free cumulant?" with P. Sniady, which appeared in Notices of the AMS, Feb. 2011. Novak also began work on a combinatorial approach to the Harish- Chandra-Itzykson-Zuber integral. In addition, he began work on a generalization of Schramm's characterization of the Poisson-Dirichlet distribution with parameter 1. After MSRI, Novak continued as a Postdoctoral Fellow at the University of Waterloo. Novak noted, “My

Novak, Jonathan experience of MSRI was certainly very positive. I had the opportunity to interact with many researchers in the field of random matrices whom I had previously known only through their publications. I learned a great deal from being able to speak with these people on a daily basis. Through the weekly seminar and the two workshops, I also gained a better sense of what the important questions in random matrix theory are, and of the direction in which the field is moving. On a professional level, it was extremely beneficial for me to be able to present my own work to seasoned researchers. I came away with a deeper understanding of how my own research programme fits into the subject as a whole, which will allow me to choose future research goals with added foresight.”

Igor Rumanov received his Ph.D. from the University of California at Davis in 2010 under the supervision of Craig A. Tracy. His dissertation was titled “Integrable Equations for Random Matrix Spectral Gap Probabilities.” While at MSRI, he and Craig A. Tracy worked on new directions in Random Matrix (RM) Theory related research, e.g. increasing importance of probabilistic methods, theory of stochastic differential equations, new applications of conditioned non-intersecting Brownian Motion models to problems of statistical mechanics and combinatorics, and the well developed theory of unitary invariant RM ensembles to physics and engineering problems. After his stay at MSRI, he continued as a Research Associate at the University of Colorado at Boulder. He finished a Rumanov, Igor publication, “All the lowest order PDE's for spectral gaps of Gaussian matrices”. He also worked on the derivation and properties of PDE's satisfied by the two-point distribution for the Airy process, obtained as a scaling limit of his previously derived PDE for two coupled finite size GUE matrices. He worked with Yang Chen on possible generalization of his approach to the derivation of PDE's for spectral gap probabilities, to non-classical unitary RME. He also started working on connections of the Asymmetric Simple Exclusion Process with the quantum XXZ chain. After MSRI, Igor Rumanov continued as a Postdoctoral Fellow at the University of Colorado at Boulder. Rumanov stated, “My experience at MSRI was very pleasant…. This gathering together of experts working on different problems is wonderful. I only wish that this could last longer - at least a whole year rather than just one semester. I am sure that the benefits of such an extension…would give more immediate, tangible results.”

Benjamin Young received his Ph.D. from the University of British Columbia in 2008. Before joining MSRI, he worked towards his post doctorate with the Centre de Recherches Mathematiques and McGill University from 2008 to 2010. While at MSRI, Young created two papers, the first titled “Domino shuffling for the Del Pezzo 3 lattice,” which was co-authored by Cyndie Cottrell. The second paper included co-authors Jim Bryan and Charles Cadman and was titled “Orbifold Topological Vertex”. Young occupied most of his time at MSRI working on 4 major new projects under the mentorship of Ken McLaughlin. Each project was centered

Young, Benjamin around his usual research area (combinatorics of perfect matchings) but were, to various degrees, influenced by the random matrix theory he had learned. Young felt that the biggest benefit during his stay was the sheer number of collaborations and the availability of so many experts in the field. After his time at MSRI, he continued as a Postdoctoral Fellow at the KTH Royal Institute of Technology in Stockholm. Young commented, “My experience at MSRI was amazing; it is an ideal place for collaboration….. My research plan looks much more fleshed out now than it did when I started. A secondary benefit of my postdoc at MSRI was the networking / career preparation opportunities that it afforded: I got a chance to practice my job talk; I met a lot of people from many different universities.” 38

Anna Zemlyanova received her Ph.D. from Lousiana State University, Baton Rouge in 2010. While at MSRI, she worked under the mentorship of Percy Deift. Her research work concentrated on applications of Riemann- Hilbert problems in elasticity and fluid mechanics. Her main goal while at MSRI was to study direct and inverse scattering theory and the steepest descent method for Riemann-Hilbert problem in connection with NLS equation, Toda Lattice and mKdV equation. She also gave a talk on “Application of Riemann-Hilbert Problems in Modelling of Cavitating Flow” in the postdoctoral seminar at MSRI. The proposed continuation of Zemlyanova, Anna her work is to apply these techniques to study the long-time behavior of the Toda lattice in the collisionless shock region. After her stay at MSRI, Zemlyanova will work as a Visiting Assistant Professor for Texas A&M University in Texas. Zemlyanova added, “Overall, the semester at MSRI was a very positive experience, and I am very thankful for the opportunity.”

Inverse Problems

Kiril Datchev received his Ph.D. from University of California, Berkeley for Prof. Maciej Zworski in 2010. While at MSRI, he worked under the mentorship of Andras Vasy. Datchev worked with him in two articles on resolvent estimates, on inverse spectral problems with Hamid Hezari (another postdoc on the program) and Ivan Ventura a student of Maciej Zworski at UC Berkeley. He also wrote a related paper with Hezari on inverse problems for resonances. He and Hezari have written a survey paper on inverse spectral problems for Inside Out II. After his stay at MSRI, Datchev continued as a CLE Moore Instructor and NSF Datchev, Kiril Postdoctoral Fellow working with his mentor, Richard Melrose, and the Massachusetts Institute of Technology.

Fernando Guevara Vasquez received his Ph.D. from Rice University in 2006 under the supervision of Liliana Borcea. While at MSRI, he worked on various projects under the mentorship of Amir Dembo. While at MSRI, he worked under the mentorship of Liliana Borcea. He worked with her and Alexander Mamonov, another postdoc in the program, in the EIT program for discrete networks. Also jointly with Druskin, they wrote a survey paper on this topic for Inside Out. He also wrote with Graeme Milton and other collaborators some papers on cloaking. After joining MSRI, he continued his work at the University of Utah as a Guevara Vasquez, tenure-tracked assistant professor. Fernando 31

Pilar Herreros received her Ph.D. from the University of Pennsylvania in 2009 under the supervision of Christopher Croke. While at MSRI, she worked under the mentorship of Gunther Uhlmann. She studied the lens rigidity problem and wrote with Croke a paper on less rigidity for two dimensional manifolds with trapped geodesics. After her stay at MSRI, Pilar Herreros continued as a Research Scholar for Mathematisches Institut Westfälische Wilhelms Universität in Münster , Germany. Herreros, Pilar

Hamid Hezari received his Ph.D. from John Hopkins University in 2009 under the supervision of Steve Zelditch. While at MSRI, he worked under the mentorship of Peter Kuchment. He collaborated with Kiril Datchev in several projects on inverse spectral problems and inverse problems for resonances. He also worked on other projects on spectral theory. After his stay at MSRI, Hezari continued on as a CLE Moore Instructor for the Massachusetts Institute of Technology.

Hezari, Hamid

Alexander Mamonov received his Ph.D. from Rice University in 2010 under the supervision of Liliana Borcea. While at MSRI, he worked under the mentorship of Liliana Borcea. Mamonov worked on discrete EIT and wrote a paper on discrete networks. After joining MSRI, Mamonov became a postdoctoral fellow for the University of Texas at Austin under the mentorship of Richard Tsai and Kui Ren.

Mamonov, Alexander

Linh Nguyen received his Ph.D. from Texas A&M University in 2010. While at MSRI, he worked under the mentorship of Maarten de Hoop. He worked on the problem of recovering the sound speed in TAT. He also studied the range characterization for a spherical mean transform on spaces of constant curvature. After joining MSRI, Nguyen became an assistant professor for the University of Idaho.

Nguyen, Linh

Juha-Matti Perkkio received his Ph.D. from Helsinki University of Technology, Finland under the supervision of Matti Lassas and Gunther Uhlmann. While at MSRI, he worked under the mentorship of P. Stefanov. He worked on the problem of inverting the ray transform with Finsler metrics. After his stay at MSRI, Perkkio continued as an assistant for Helsinki University of Technology.

Perkkio, Juha-Matti

Leo Tzou received his Ph.D. from the University of Washington under the supervision of Gunther Uhlman. While at MSRI, he continued to work under the mentorship of Uhlmann. He worked with Colin Guillarmou, a visitor for a month, on the Calderon problem on manifolds, including the case of the magnetic Laplacian on Riemann surfaces and general two dimensional systems. After joining MSRI, Tzou continued his postdoctoral reseachship with MSRI at Stanford University

Tzou, Leo and became a tenure-tracked assistant professor for the University of Arizona.

Free Boundary Problems

John Andersson received his Ph.D. at the Kungliga Tekniska Högskolan in 2005 under the supervision of Henrik Shahgholian. At MSRI, Andersson worked on free boundary problems from the regularity point of view, under the mentorship of C.L. Evans. His interest and focus were on problems with unstable character and singularities of such problems. After his stay at MSRI, Andersson continued on at the University of Warwick in the UK.

Andersson, John

Nestor Guillen received his Ph.D. at the University of Texas at Austin in 2010 under the supervision of Luis A. Caffarelli. His dissertation was titled “Regularization In Phase Transitions With Gibbs-Thomson Law.” At MSRI, Guillen worked on problems related to the fractional laplacian under the mentorship of A. Petrosyan. His interests are also towards problems related to Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations, and Regularity for non-local almost minimal boundaries and applications. After his time at MSRI, he continued to the University of California, Los Angeles.

Guillen, Nestor 33

Guanghao Hong received his Ph.D. at Xi'an Jiaotong University in 2009 under the supervision of Lihe Wang. At MSRI, Hong worked with M. Feldman on regularity of the Alt-Caffarelli type free boundary problem, along with symmetry properties of the solutions of the elliptical equations. After his time at MSRI, he continued on to Xi'an Jiaotong University as a Lecturer.

Hong, Guanghao

Ryan Hynd received his Ph.D. at the University of California, Berkeley in 2010 under the supervision of Lawrence Craig Evans. His dissertation was titled “Partial Differential Equations with Gradient Constraints Arising In The Optimal Control of Singular Stochastic Processes”. At MSRI, Hynd worked with mentor H. Shahgholian on concavity properties of infinity-laplacian ground states and problems related to Hamilton Jacobi Equations in the Wasserstein space. His interest stretches to the analysis of eigenvalue problem of singular ergodic control. After his time at MSRI, he continued on to the Courant Institute Hynd, Ryan of Mathematical Science.

Erik Lindgren received his Ph.D. at Kungliga Tekniska Högskolan in 2009 under the supervision of Henrik Shahgholian. His dissertation was titled “Regularity Properties Of Two-phase Free Boundary Problems”. At MSRI, Lindgren worked with mentor A. Petrosyan on optimal regularity aspects in free boundary problems, specially the no-sign obstacle problem, boundary behavior and poinstwise estimates. He has some recent interest towards infinity-laplace equation. After his time at MSRI, he continued on to the University of Trondheim.

Lindgren, Erik

Henok Mawi received his Ph.D. at Temple University in 2010 under the supervision of Cristian Gutierrez. At MSRI, Mawi worked with mentor M. Feldman on Monge Ampere equations and related problems. He also started looking at problems in free boundaries related to biharmonic operators. After his time at MSRI, he continued on to be a Lecturer at Howard University.

Mawi, Henok

Betul Orcan received her Ph.D. from the University of Texas at Austin in 2010 under the supervision of Luis A. Caffarelli. Her dissertation was titled “About The Geometry And Regularity of Largest Subsolutions For A Free Boundary Problem In R2: Elliptic Case”. While at MSRI, Orcan spent time learning about regularity of free boundary problems, as well as homogenization of the free boundary problem in random media under the mentorship of H. Shahgholian. Her current interest is towards the regularity and geometry of viscosity solutions for fully nonlinear free boundary problems and homogenization problems in Geometric Measure Orcan, Betul Theory. After MSRI, she continued on to Rice University.

Ko Woon Um received her Ph.D. from the University of Iowa in 2009 under the supervision of Lihe Wang. While at MSRI, Um worked with her mentor C.L. Evans on elliptic equations with singular BMO coefficients in Reifenberg domains and also regularity for porous medium type equations with divergence-free drift. After MSRI, she continued on as a Lecturer at the University of Texas at Austin.

Um, Ko Woo

Arithmetic Statistics

Jonathan Bober received his Ph.D. from the University of Michigan in 2009. Before joining MSRI, he was associated with the Institute for Advanced Study. While at MSRI, he worked under the mentorship of Michael Rubinstein where he published “Bounds for large gaps between zeros of L-functions”. Other publications include “The distribution of the maximum of character sums” with Leo Goldmaker and “New computations of Reimann zeta function” with Ghaith Hiary. He enjoyed the wekly seminars and working in groups with other fellow colleagues of MSRI. After his stay, he worked with the University of Washingtion as a visiting scholar. Bober, Jonathan

Alina Bucur received her Ph.D. from Brown University in 2006. Before joining MSRI, she was an instructor for the Massachusettes Institute of Technology. While at MSRI, she worked under the mentorship of Kiran Kedlaya as she published “Zeta functions of Artin-Schreier curves over finite fields” with Chantal David, Brooke Feigon, Matilde Lalin and Keneenika Sinha. Other publications she worked on include “D4 curves over finite fields” with Daniel Erman and Melanie Wood. After her time at MSRI, she continued as an assistant professor for the University of California, San Diego. Bucur, Alina

Brooke Feigon received her Ph.D. from the University of California, Los Angeles in 2006. Before joining MSRI, she pursued her post-doc at the University of Toronto and the Institute for Advanced Study. She continued as an assistant professor for the University of East Anglia. While at MSRI, she worked under the mentorship of Harold Stark. After her time at MSRI, she continued as an assistant professor for the University of East Anglia and as an assistant for the College of New York, CUNY.

Feigon, Brooke

Ghaith Hiary received his Ph.D. from the University of Minnesota in 2008. Before joining MSRI, he was associated with the University of Waterloo, IAS. While at MSRI, he worked under the mentorship of D.W. Farmer as he published several works. These included “Numerical study of the derivative of the reimann zeta function at zeros” with A.M. Odlyzko and “Uniforme asymptotics for the full moment conjecture of the Riemann zeta function with M.O. Rubinstein. In addition he published “Computing Dirichlet character sums to a powerful modules” and “Numerical behavior of the zeta function at large values” with J.W. Bober. He found the numerous informal discussion session and various lectures by invited Hiary, Ghaith visotors at MSRI very interesting and beneficial. After his stay at MSRI, he

continued on to the University of Bristol.

Sonal Jain received his Ph.D. from Harvard University in 2007. Before joining MSRI, he was an instructor for the Courant Institute. While at MSRI, he worked under the mentorship of Barry Mazur. He felt that the impressive group of senior faculty by whom he had built new collaborations with was extremely beneficial in extending his work in new directions. After his stay at MSRI, he continued as an instructor for the Courant Institute.

Jain, Sonal

Robert Miller received his Ph.D. from the University of Washington in 2010. While at MSRI, he worked under the mentorship of John Cremona. After his stay at MSRI, he worked as a senior software engineer for quid.com.

Miller, Robert

Kaneenika Sinha received her Ph.D. from Queen’s University, Kingston, Ontario, Canada in 2006. Before joining MSRI, she worked as a post doctorate fellow at the University of Toronto, PIMS Postdoctorate fellow at University of Alberta, and as an Assistant Professor at Indian Institute of Science Educationa and Research Kolkata, Indiana. While at MSRI, she worked under the mentorship of Henryk Iwaniec with whom she published “The non-vanishing of central values of Rankin-Selbery L-functions.” She felt that her stay at MSRi was very beneficial and highly conducive to learning and research. After his stay at MSRI, she continued as an Assistant Professor at Indian Institute of Science Education. Sinha, Kaneenika

Fredrik Stromberg received his Ph.D. from Uppsala University in 2005. Before joining MSRI, he purused his post doctorate degree at TU Clausthal and TU Darmstadt. While at MSRI, he worked under the mentorship of Nils- Peter Skoruppa with whome he published “Newforms and spectral multiplicities for Г0(9)” and “Dimension formulas for vector valued Hilbert modular forms”. He felt the MSRI program was great and gave him the opportunity to meet and interact with many leading researchers in the filed. After his stay at MSRI, he continued his postdoc at TU Darmstadt.

Stromberg, Fredrik

Gonzalo Tornaria received his Ph.D. from the University of Texas, Austin in 2005. Before joining MSRI, he worked at the Universite de Montreal and Universidad de la Republica. While at MSRI, he worked under the mentorship of Jonathan Hanke as he published numerous works including “ABocherer-Type conjecture for Paramodular Forms” and “Central values of L-series for Siegel Modular and Paramodular Forms” with Nathan Ryan, Int J Number theory 7. He also published “Formal Siegel Modular Forms” and “Siegel modular forms package” with Martin Raum, Nathan Ryan, and Nils Skoruppa. After his stay at MSRI, he continued at the Universidad de la Republica. Tornaria, Gonzalo

Complementary Program 2010-11

Jacob White received his Ph.D. from Arizona State University in August 2010 under the supervision of Hélène Barcelo. His dissertation was titled “On the Complement of R-Disjoint K-Parabolic Subspace Arrangements.” While at MSRI, White finished writing up several papers for submission. The first is titled "Pentagonal Relations and the Exchange Module of the type A_n Cluster Algebra", which is joint work with Hélène Barcelo, and Christopher Severs. White also submitted another paper, "On the Homology of the Real Complement of the k-Parabolic Arrangement" which is joint work with Christopher Severs. Motivated by some conversations with

White, Jacob Matthias Beck, of San Francisco State University, White investigated a multivariate chromatic polynomial associated to hypergraphs. The results of this investigation have been written up in a paper titled “On Multivariate Chromatic Polynomials of Hypergraphs and Hyperedge Elimination”, and has been submitted to journal. While at MSRI, White also continued studying Hopf monoids in the category of graphical species, a project that is currently being written up for publication. Portions of this work were done in collaboration with Marcelo Aguiar. White also proved several results regarding the topology of simplicial complexes coming from the study of signed graphs. These results, obtained with Christopher Severs, are being written up for submission. Finally, White engaged in collaboration with Fatemeh Mohammadi, and Volkmar Welker, during their visits to the MSRI. These collaborations investigated problems in combinatorial commutative algebra, and are still unfinished and ongoing work. After leaving MSRI, White accepted a one year postdoctoral position at Arizona State University,

in Tempe, Arizona.

3.2 Postdoctoral Fellow Placement List

Name (Last, First) Placement Institution Name Placement Department Placement Position Country Andersson, John University of Warwick Mathematics Assistant Professor UK Bender, Martin Institut Mittag-Leffler Mathematics Postdoc Sweden Bober, Jonathan University of Washington Mathematics Visiting Scholar US Bucur, Alina University of California, San Diego Mathematics Assistant Professor US Feigon, Brooke College of New York, CUNY Mathematics Assistant US Guevara Vasquez, FernandoUniversity of Utah Mathematics Assistant Professor US Guillen, Nestor University of California, Los Angeles Mathematics E.R. Hedrick Assistant Professor US Herreros, Pilar Mathematisches Institut Westfälische Wilhelms Universität Mathematics Research Scholar Germany Hezari, Hamid Massachusetts Institute of Technology Mathematics CLE Moore Instructor US Hiary, Ghaith University of Bristol Mathematics Postdoctoral Associate UK Hong, Guanghao Xi'an Jiaotong University Mathematics Lecturer China Jain, Sonal Courant Institute Mathematics Instructor US Liechty, Karl University of Michigan Mathematics Postdoctoral Assistant Professor US Lindgren, Erik University of Trondheim Mathematics Postdoc Norway Mamonov, Alexander University of Texas, Austin Mathematics Postdoctoral Fellow US Mawi, Henok Howard University Mathematics Lecturer US Miller Robert Quid.com N/A Software Engineer US Nguyen, Linh University of Idaho Mathematics Assistant Professor US Nordenstam, Eric University of Vienna Mathematics Postdoc Austria Novak, Jonathan University of Waterloo Mathematics Postdoctoral Fellow Canada Orcan, Betul Rice University Mathematics G.C. Evans Instructor US Perkkio, Juha-Matti Helsinki University of Technology Mathematics Assistant Finland Rumanov, Igor University of Colorado at Boulder Mathematics Research Associate US Sinha, Kaneenika Indian Institute of Science Education Mathematics Assistant Professor India Stromberg, Fredrik TU Darmstadt Mathematics Postdoc Germany Tornaria, Gonzalo Universidad de la Republica Mathematics Assistant Professor Uruguay Tzou, Leo University of Arizona Mathematics Assistant Professor US Um, Ko Woon University of Texas, Austin Mathematics Lecturer US White, Jacob Arizona State University Mathematics Postdoc US Young, Benjamin KTH Royal Institute of Technology Mathematics Postdoctoral Fellow Sweden Zemlyanova, Anna Texas A&M University Mathematics Visiting Assistant Professor US

2010–1 Postdocs’ Home Institution (based on AMS Groupings)

3.3 Postdoctoral Fellow Participant Summary # of Citizens # of & Perm. # of # of US Home Programs Postdocs Res. % Female % Minorities1 % Institution % Random Matrix Theory, Interacting Particle Systems and Integrable Systems 7 2 28.6% 1 14.3% 0 0% 3 42.9% Inverse Problems and Applications 7 0 0.0% 1 14.3% 0 0% 4 57.1% Free Boundary Problems, Theory and Applications 7 1 14.3% 2 28.6% 0 0% 4 57.1% Arithmetic Statistics 9 5 71.4% 3 33.3% 0 0% 4 44.4% Complementary Program 2010-11 1 1 14.3% 0 0.0% 0 0% 1 100.0%

Total # of Distinct Postdocs 31 9 29.0% 7 22.6% - 0.0% 16 51.6% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

Yrs since PhD # of PD Years since PhD 0 11 12 1 7 10 2 3 3 2 8 4 4 6 5 3 4 # # postdocs of 6 0 2 7 1 0 Total 31 0 1 2 3 4 5 6 7 # of years

3.4 Postdoctoral Fellow Demographic Data

2010–11 Postdoctoral Fellows Demographic Summary

% (No Decl.)* % 3% Gender # Male # of Distinct PD 31 100.0% 23% Male 23 76.67% 74.2% Female 7 23.33% 22.6% Female 74% Decline to State Gender 1 3.2% Decline to State Gender

Ethnicities # % (No Decl.)* % Native American Native American 0 0.00% 0.0% Asian Asian 2 11.76% 6.5% Black 0 0.00% 0.0% Black 38.7% Hispanic 2 11.76% 6.5% 38.7% Hispanic Pacific 1 5.88% 3.2% White 12 70.59% 38.7% Pacific 6.5% 6.5% Decline to State Ethnicities 12 38.7% White Unavailable Information 2 6.5% 3.2% 6.5% 0.0% 0.0% Decline to State Minorities - 0.0% Ethnicities Unavailable Information

Citizenships # % US Citizen & Perm. Residents 9 29.0% Foreign 22 71.0% Unavailable information 0 0.0% # of Distinct PD 31 100.0% Home Inst. in 50% 50% US US Citizen 8 25.8% Home Inst. Perm Residents 1 3.2% NOT in US Home Inst. in US 16 51.61%

Year of Ph.D # % 2011 & Later 0 0.0% 2010 11 35.5% 2005-2009 19 61.3% 2000-2004 1 3.2% 61% 1995-1999 0 0.0% 2010 1990-1994 0 0.0% 2005-2009 1985-1989 0 0.0% 36% 3% 1981-1984 0 0.0% 2000-2004 1980 & Earlier 0 0.0% Unavailable Info. 0 0.0% Total # of Distinct PD 31 100.0%

*Statistic Calculation based on all participants that did not decline.

2010–11 Postdoctoral Fellows Home Institution Classified by States *Regions based on US Census classification 2007 Census State # % Population South 6 37.5% 36.6% AL - 0.0% 1.5% AR - 0.0% 0.9% DE - 0.0% 0.3% DC 1 6.3% 0.2% South West FL - 0.0% 6.1% 37% 31% GA - 0.0% 3.2% KY - 0.0% 1.4% LA - 0.0% 1.4% Midwest MD - 0.0% 1.9% Northeast 13% MS - 0.0% 1.0% 19% NC - 0.0% 3.0% OK - 0.0% 1.2% SC - 0.0% 1.5% TN - 0.0% 2.0% TX 5 31.3% 7.9% VA - 0.0% 2.6% WV - 0.0% 0.6% West 5 31.3% 23.2% AK - 0.0% 0.2% AZ 1 6.3% 2.1% HI - 0.0% 0.4% ID - 0.0% 0.5% MT - 0.0% 0.3% CA 2 12.5% 12.1% CO - 0.0% 1.6% NV - 0.0% 0.9% NM - 0.0% 0.7% OR - 0.0% 1.2% UT 1 6.3% 0.9% WA 1 6.3% 2.1% WY - 0.0% 0.2% Midwest 2 12.5% 22.0% IL - 0.0% 4.3% IN 1 6.3% 2.1% IA 1 6.3% 1.0% KS - 0.0% 0.9% MI - 0.0% 3.3% MN - 0.0% 1.7% MO - 0.0% 1.9% ND - 0.0% 0.2% NE - 0.0% 0.6% OH - 0.0% 3.8% SD - 0.0% 0.3% WI - 0.0% 1.9% Northeast 3 18.8% 18.1% CT - 0.0% 1.2% ME - 0.0% 0.4% MA 1 6.3% 2.1% NH - 0.0% 0.4% NJ 1 6.3% 2.9% NY 1 6.3% 6.4% PA - 0.0% 4.1% RI - 0.0% 0.4% VT - 0.0% 0.2% Total 16 100% 100% 42

2010–11 Postdoctoral Fellows Home Institution Classified by Countries *Regions based on United Nations classification

Americas 20 North America Canada 3 United States 16 South America Uruguay 1 Asia 2 East Asia China 1 South-central Asia India 1 Europe 9 Northern Europe England 2 Finland 2 Norway 1 Western Europe Belgium 2 Germany 2 Grand Total 31

Americas 65%

Europe 29% Asia 6%

3.5 Postdoctoral Research Member Placement List

Name (Last, First) Placement Institution Name Placement Department Placement Position Country Bae, Myoungjean Northwestern University Mathematics Boas Assistant Professor US Datchev, Kiril Massachusetts Institute of Technology Mathematics CLE Moore Instructor US Gualdani, Maria Pia The University of Texas at Austin Mathematics Research Assistant Professor US Holowinsky, Roman The Ohio State University Mathematics Assistant Professor US Huynh, Duc Khiem University of Waterloo Pure Mathematics Postdoctoral Fellow Canada Hynd, Ryan Courant Institute of Mathematical Science Mathematics Postdoctoral Fellow US Kargin, Vladislav Stanford University Mathematics Szego Assistant Professor US Mahlburg, Karl Lousiana State University Mathematics Assistant Professor US Munshi, Ritabrata Tata Institute of Fundamental Research Mathematics Professor India Rhoades, Robert Stanford University Mathematics Postdoc US Sengun, Mehmet Max Planck Institute for Mathematics Mathematics Visitor Germany Sire, Yannick University Aix-Marseille III - Paul Cezanne Laboratory of Analysis, Topology and Probability Assistant Professor France Visan, Monica University of California, Los Angeles Mathematics Assistant Professor US Wood, Melanie Stanford University Mathematics Szego Assistant Professor US Yang, Andrew Dartmouth College Mathematics Instructor US

3.6 Postdoctoral Research Member Summary # of US Citizens Home # of & Perm. # of # of Instituti Programs PDRM Res. % Female % Minorities % on % Random Matrix Theory, Interacting Particle Systems and Integrable Systems 1 0 0.0% 0 0.0% 0 0.0% 1 100.0% Inverse Problems and Applications 1 1 100.0% 0 0.0% 0 0.0% 1 100.0% Free Boundary Problems, Theory and Applications 5 2 40.0% 3 60.0% 1 50.0% 4 80.0% Arithmetic Statistics 8 5 62.5% 1 12.5% 0 0.0% 5 62.5% Complementary Program 2010-11 0 0 0.0% 0 0.0% 0 0.0% 0 0.0%

Total # of Distinct Postdoc Research Members 15 8 53.3% 4 26.7% 1 12.5% 11 73.3% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

4. Graduate Program

In 2010–11, 530 graduate students visited MSRI to participate in our workshops (318 graduate students), summer graduate schools (188 graduate students), and programs (24 graduate students). While the majority of the graduate students who visit MSRI had been invited to take part in one of our workshops or summer graduate schools, a smaller number of graduate students were invited as ‘Program Associates’ in our semester- and year-long scientific programs.

4.1 Summer Graduate Schools (SGS)

Every summer, MSRI organizes several summer graduate schools (usually two weeks each), most of which are held at MSRI. Attending one of these schools can be a very motivating and exciting experience for a student; participants have often said that it was the first experience where they felt like real mathematicians, interacting with other students and mathematicians in their field.

Graduate students from MSRI Academic Sponsoring Institutions or from Department of Mathematics at U.S. Universities are eligible for summer schools. For each institution, MSRI provides support for two students per summer and for a third student if at least one of the students is female or from a group that is underrepresented in the mathematical sciences. MSRI covers travel and local expenses with the maximal allowance for travel reimbursement being

$550 for students from U.S. and Canadian universities (depending on the point of origin), and $700 for students from other sponsoring institutions.

The application procedure is as follows: The summer graduate schools and the open enrollment period for the summer of year n+1 are announced in October of year n. Graduate students must be nominated by their Director of Graduate Studies during the enrollment period. MSRI accepts nominees on a first-come first-served basis up to the limits of the capacity of each workshop, which is around 40 for workshops that are held at MSRI. If the chosen workshop is already full, the students are either kept on a waiting list or the nominating institution may make nominations to other workshops until its workshop quota is reached.

The following is a list of the six Summer Graduate Schools that took place during the 2010 summer. Eighty-four (84) institutions nominated a total of 205 students. Altogether 24 lecturers and 188 graduate students participated in these workshops. Of those graduate students, 31% were female. See the table in section 4.2 for detailed demographic data.

For a complete report on each SGS, please refer to the Appendix.

SGS 2: Sage Days 22: Elliptic Curves June 21, 2010 to July 2, 2010 Organized by William Stein (University of Washington)

4.2 Summer Graduate Schools Data

Participant List (See e-mail attached file)

Participant Summary

# of Citizens # of & Perm. # of # of US Home Summer Graduate Schools Participants Res. % Female % Minorities1 % Institution % Algebraic, Geometric, and Combinatorial Methods for Optimization 40 20 50.0% 14 35.0% 0 0.0% 33 82.5% IAS/PCMI Research Summer School 2010: Image Processing 20 7 35.0% 7 35.0% 0 0.0% 17 85.0% Mathematics of Climate Change 30 18 60.0% 12 40.0% 2 11.8% 27 90.0% Probability workshop: 2010 PIMS Summer School in Probability. 39 16 41.0% 13 33.3% 0 0.0% 33 84.6% Sage Days 22: Computing with Elliptic Curves 50 31 62.0% 11 22.0% 0 0.0% 46 92.0% Summer School on Operator Algebras and Noncommutative Geometry 9 4 44.4% 2 22.2% 1 50.0% 7 77.8%

Total # of Distinct Participants 188 96 51.1% 59 31.4% 3 3.4% 163 86.7% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

2010–11 Summer Graduate Schools Demographic Summary

% (No Gender # Decl.)* % # of Distinct Participants 188 100.0% 69% Male 129 68.62% 68.6% Female 59 31.38% 31.4% Male Decline to State Gender 0 0.0% Female 31%

% (No Decl.)* % Ethnicities # Asian Native American 0 0.00% 0.0% 7% Asian 78 44.32% 41.5% Black Black 3 1.70% 1.6% 41% Hispanic 5 2.84% 2.7% Pacific 0 0.00% 0.0% 48% Hispanic White 90 51.14% 47.9% Decline to State Ethnicities 13 6.9% White Unavailable Information 0 0.0% 1% 3% Decline to State Minorities 3 3.4% Ethnicities

Citizenships # % US Citizen & Perm. Residents 96 51.1% Foreign 92 48.9% Unavailable information 0 0.0% # of Distinct Participants 188 100.0% 87% Home Inst. in US

US Citizen 89 92.7% 13% Home Inst. NOT Perm Residents 7 100.0% in US

Home Inst. in US 163 86.70%

*Statistic Calculation based on all participants that did not decline.

Summer Graduate Schools Algebraic, Geometric, and Combinatorial Methods for Optimization IAS/PCMI Research Summer School 2010: Image Processing Mathematics of Climate Change Probability workshop: 2010 PIMS Summer School in Probability. Sage Days 22: Computing with Elliptic Curves Summer School on Operator Algebras and Noncommutative Geometry

2010–11 Summer Graduate Schools Home Institution Classified by States *Regions based on US Census classification 2007 Census State #% Population South 43 26.4% 36.6% AL - 0.0% 1.5% AR - 0.0% 0.9% 19% 26% South DE - 0.0% 0.3% DC 1 0.6% 0.2% 25% West FL 1 0.6% 6.1% 30% Midwest GA 10 6.1% 3.2% KY 2 1.2% 1.4% Northeast

LA 5 3.1% 1.4% MD 1 0.6% 1.9% MS - 0.0% 1.0% NC 8 4.9% 3.0% OK 3 1.8% 1.2% SC 3 1.8% 1.5% TN - 0.0% 2.0% TX 7 4.3% 7.9% VA 2 1.2% 2.6% WV - 0.0% 0.6% West 49 30.1% 23.2% AK - 0.0% 0.2% AZ 2 1.2% 2.1% HI - 0.0% 0.4% ID - 0.0% 0.5% MT - 0.0% 0.3% CA 35 21.5% 12.1% CO 4 2.5% 1.6% NV - 0.0% 0.9% NM - 0.0% 0.7% OR 5 3.1% 1.2% UT - 0.0% 0.9% WA 3 1.8% 2.1% WY - 0.0% 0.2% Midwest 41 25.2% 22.0% IL 10 6.1% 4.3% IN 7 4.3% 2.1% IA 1 0.6% 1.0% KS 4 2.5% 0.9% MI 8 4.9% 3.3% MN 4 2.5% 1.7% MO 1 0.6% 1.9% ND - 0.0% 0.2% NE 3 1.8% 0.6% OH 1 0.6% 3.8% SD - 0.0% 0.3% WI 2 1.2% 1.9% Northeast 30 18.4% 18.1% CT 4 2.5% 1.2% ME - 0.0% 0.4% MA 9 5.5% 2.1% NH 3 1.8% 0.4% NJ - 0.0% 2.9% NY 8 4.9% 6.4% PA 3 1.8% 4.1% RI 3 1.8% 0.4% VT - 0.0% 0.2% Other - 0.0% 0% PR - 0.0% 0% Other - 0.0% 0% Total 163 100% 100% 48

2010–11 Summer Graduate Schools Home Institution Classified by Countries *Regions based on United Nations classification

Americas 173 Central America Mexico 1 North America Canada 8 United States 163 South America Colombia 1 Asia 8 East Asia China 2 Korea, Republic of 5

Mongolia 1 Europe 6 Northern Europe England 2 Iceland 2 Southern Europe Italy 1 Western Europe France 1 Unavailable information 1 Grand Total 188

Americas 92% Asia

Europe

Unavailable 1% information 3% 4%

4.3 Program Associates

Program Associates benefit greatly from the opportunity to interact with leaders of a field and postdoctoral fellows, gaining intense exposure to current ideas and trends in their area of specialization. While MSRI does not have the financial resources to fund the Program Associates, they are closely supervised and essentially benefit from all members’ privileges. They are provided with an access card to the building which allows them to use the premises at any time. They receive a bus pass, and a library and sports facilities access pass. There were 24 graduate students who resided at MSRI for an extended period of time during the academic year 2010–11. Of those students, 21% were female. See the table in section 4.4 for a detailed description of the demographic data.

The Fall semester program in Inverse Problems and Applications and the Spring semester program in Arithmetic Statistics hosted the majority of the program associates.

In the Inverse Problems and Applications Program, graduate students, postdocs, and researchers were presented a wide panorama of inverse problems and topics, mathematical techniques, applications and outstanding challenges. In the research workshop that took place during this program, eight talks were delivered by postdocs and graduate students. The talks, which attracted a large audience, gave a spectacular overview of many theoretical and applied contemporary issues of the area.

In the Random Matrix Theory Program, many graduate students attended the seminars for the duration of their advisors’ visits. Corwin and Auffinger were in residence for most of the semester. Corwin, though still a graduate student, was chosen to give one of the Evans Lectures in the Mathematics Department at UC Berkeley. He has an impressive list of publications and is one of the rising stars in the field.

In the Free Boundary Problems Program, four graduate students belonged to Shahgholian’s group. Along with the postdocs, they participated in seminars in the Evans Lectures series and the seminars at MSRI.

The Arithmetic Statistics Program saw a large number of graduate students participated as program associates. Manjul Bhargava, working with his graduate student Arul Shankar, discovered and proved that a positive proportion of all plane cubics fail the Hasse principle. This principle asserts the existence of rational solutions to Diophantine equations given the existence of local solutions. The fact that this principle often fails came as a surprise to many.

4.4 Program Associates Data

Participant List

Program Home Institution Activity Associate Auffinger, Antonio New York University Random Matrix Theory, Interacting Particle Systems and Integrable Systems Corwin, Ivan New York University Random Matrix Theory, Interacting Particle Systems and Integrable Systems Geudens, Dries Katholieke Universiteit Leuven Random Matrix Theory, Interacting Particle Systems and Integrable Systems Hardy, Adrien Katholieke Universiteit Leuven Random Matrix Theory, Interacting Particle Systems and Integrable Systems Male, Camille École Normale Supérieure de Lyon Random Matrix Theory, Interacting Particle Systems and Integrable Systems Blasten, Eemeli University of Helsinki Inverse Problems and Applications Gallardo, Ricardo Rice University Inverse Problems and Applications Oksanen, Lauri University of Helsinki Inverse Problems and Applications Thomas, Ashley Rensselaer Polytechnic Institute Inverse Problems and Applications Lynne Zhou, Ting University of Washington Inverse Problems and Applications Zubeldia, Miren Universidad del Pais Vasco/Euskal Inverse Problems and Applications Herriko Unibertsitatea Bazarganzadeh, Stockholm University Free Boundary Problems, Theory and Applications Mahmoudreza Minne, Andreas Royal Institute of Technology (KTH) Free Boundary Problems, Theory and Applications Sajadini , Sadna Royal Institute of Technology (KTH) Free Boundary Problems, Theory and Applications Stromqvist, Martin KTH Royal Institute of Technology Free Boundary Problems, Theory and Applications Alderson, Matthew University of Waterloo Arithmetic Statistics Bettin, Sandro University of Bristol Arithmetic Statistics Boylan, Hatice Bilkent University Arithmetic Statistics Kane, Daniel Harvard University Arithmetic Statistics Rishikesh, University of Waterloo Arithmetic Statistics Sekhon, Gagan University of Connecticut Arithmetic Statistics Deep Weigandt, James Purdue University Arithmetic Statistics Wilson, Kevin Princeton University Arithmetic Statistics Yamagishi , University of Waterloo Arithmetic Statistics Shuntaro

Program Associates Demographic Data

# of Citizens & Perm. # of # of US Home Programs # of PA Res. % Female % Minorities % Institution % Random Matrix Theory, Interacting Particle Systems and Integrable Systems 5 1 20.0% 0 0.0% 0 0.0% 2 40.0% Inverse Problems and Applications 6 1 16.7% 3 50.0% 0 0.0% 3 50.0% Free Boundary Problems, Theory and Applications 4 0 0.0% 1 25.0% 0 0.0% 0 0.0% Arithmetic Statistics 9 4 44.4% 1 11.1% 0 0.0% 4 44.4% Complementary Program 2010-11 0 0 0.0% 0 0.0% 0 0.0% 0 0.0%

Total # of Distinct Program Associates 24 6 25.0% 5 20.8% - 0.0% 9 37.5% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

2010–11 Program Associates Demographic Summary

% (No Gender # Decl.)* % # of Distinct Program Assoc. 24 100.0% 79% Male 19 79.17% 79.2% Male Female 5 20.83% 20.8% Decline to State Gender 0 0.0% Female 21%

% (No Ethnicities # Decl.)* % Native American 0 0.00% 0.0% Asian 2 22.22% 8.3% Asian Black 0 0.00% 0.0% 87.5% Hispanic 1 11.11% 4.2% Hispanic Pacific 0 0.00% 0.0% 25.0% White 6 66.67% 25.0% White Decline to State Ethnicities 0 0.0% Unavailable Information 21 87.5% Unavailable Information Minorities 0 0.0% 8.3% 4.2%

Citizenships # % US Citizen & Perm. Residents 6 25.0% Foreign 18 75.0% Unavailable information 0 0.0% # of Distinct Program Assoc. 24 100.0% 37% Home Inst. in US US Citizen 6 25.0% 63% Perm Residents 0 0.0% Home Inst. NOT in US Home Inst. in US 9 37.50%

*Statistic Calculation based on all participants that did not decline.

2010–11 Program Associates Home Institution Classified by States *Regions based on US Census classification

2007 Census State #% Population South 1 11.1% 36.6% AL - 0.0% 1.5% South AR - 0.0% 0.9% 11% DE - 0.0% 0.3% West DC - 0.0% 0.2% 11% FL - 0.0% 6.1% GA - 0.0% 3.2% KY - 0.0% 1.4% Northeast LA - 0.0% 1.4% 67% MD - 0.0% 1.9% MS - 0.0% 1.0% NC - 0.0% 3.0% Midwest OK - 0.0% 1.2% 11% SC - 0.0% 1.5% TN - 0.0% 2.0% TX 1 11.1% 7.9% VA - 0.0% 2.6% WV - 0.0% 0.6% West 1 11.1% 23.2% AK - 0.0% 0.2% AZ - 0.0% 2.1% HI - 0.0% 0.4% ID - 0.0% 0.5% MT - 0.0% 0.3% CA - 0.0% 12.1% CO - 0.0% 1.6% NV - 0.0% 0.9% NM - 0.0% 0.7% OR - 0.0% 1.2% UT - 0.0% 0.9% WA 1 11.1% 2.1% WY - 0.0% 0.2% Midwest 1 11.1% 22.0% IL - 0.0% 4.3% IN 1 11.1% 2.1% IA - 0.0% 1.0% KS - 0.0% 0.9% MI - 0.0% 3.3% MN - 0.0% 1.7% MO - 0.0% 1.9% ND - 0.0% 0.2% NE - 0.0% 0.6% OH - 0.0% 3.8% SD - 0.0% 0.3% WI - 0.0% 1.9% Northeast 6 66.7% 18.1% CT 1 11.1% 1.2% ME - 0.0% 0.4% MA 1 11.1% 2.1% NH - 0.0% 0.4% NJ 1 11.1% 2.9% NY 3 33.3% 6.4% PA - 0.0% 4.1% RI - 0.0% 0.4% VT - 0.0% 0.2% Other - 0.0% 0% PR - 0.0% 0% Other - 0.0% 0% Total 9 100% 100%

2010–11 Program Associates Home Institution Classified by Countries *Regions based on United Nations classification

Americas 12 North America Canada 3 United States 9 Asia 1 46% Western Asia Turkey 1 50% Americas Europe 11 Northern Europe England 1 Asia Finland 2 4% Europe Sweden 4 Southern Europe Spain 1 Western Europe Belgium 2 France 1 Grand Total 24

4.5 Graduate Students List (Participants who attended 2010–11 workshops, excluding Summer Graduate Schools) (See e-mail attached file)

4.6 Graduate Students Data (Participants who attended 2010–11 workshops, excluding Summer Graduate Schools)

# of US Citizens Home # of & Perm. # of # of Instituti Workshops Participants Res. % Female % Minorities1 % on % 16 Scientific Workshops Arithmetic Statistics Research 19 10 52.6% 4 21.1% 0 0.0% 10 52.6% Connections for Women: An Introduction to Random Matrices 19 4 21.1% 8 42.1% 0 0.0% 8 42.1% Connections for Women: Arithmetic Statistics 8 6 75.0% 6 75.0% 0 0.0% 7 87.5% Connections for Women: Free Boundary Problems, Theory and Applications 8 0 0.0% 3 37.5% 0 0.0% 7 87.5% Connections for Women: Inverse Problems and Applications 18 8 44.4% 11 61.1% 0 0.0% 16 88.9% Free Boundary Problems, Theory and Applications Research 14 5 35.7% 2 14.3% 0 0.0% 11 78.6% Introductory Workshop on Inverse Problems and Applications 38 11 28.9% 15 39.5% 0 0.0% 30 78.9% Introductory Workshop: Arithmetic Statistics 20 15 75.0% 4 20.0% 1 7.1% 17 85.0% Introductory Workshop: Free Boundary Problems, Theory and Applications 16 4 25.0% 4 25.0% 0 0.0% 13 81.3% Inverse Problems: Theory and Applications Research 30 6 20.0% 10 33.3% 0 0.0% 20 66.7% Random Matrix Theory and Its Applications I 41 13 31.7% 7 17.1% 0 0.0% 27 65.9% Random Matrix Theory and its Applications II 27 11 40.7% 4 14.8% 0 0.0% 21 77.8% 21st Bay Area Discrete Math Day (BADMath Day) 21 18 85.7% 5 23.8% 2 11.1% 20 95.2% Bay Area Differential Geometry (BADG) Seminar Fall 2010 1 1 100.0% 0 0.0% 0 0.0% 1 100.0% Hot Topics: Kervaire invariant 13 7 53.8% 5 38.5% 0 0.0% 10 76.9% SIAM/MSRI workshop on Hybrid Methodologies for Symbolic-Numeric Computation 4 3 75.0% 1 25.0% 0 0.0% 3 75.0% All 19 Workshops Total 297 122 41.1% 89 30.0% 3 2.5% 221 74.4%

3 Education & Outreach Workshops Circle on the Road Spring 2011 9 5 55.6% 1 11.1% 0 0.0% 7 77.8% Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers 10 9 90.0% 3 30.0% 0 0.0% 9 90.0% Workshop on Mathematics Journals 2 2 100.0% 0 0.0% 0 0.0% 2 100.0% All 19 Workshops Total 21 16 76.2% 4 19.0% - 0.0% 18 85.7%

All 19 Workshops Total 318 138 43.4% 93 29.2% 3 2.3% 239 75.2% 1 Minorities are US citizen who declare themselves American Indian, Black, Hispanic, or Pacific Islander. Minority percentage is calculated by dividing the number of Minorities by the total number of US citizens.

5. Undergraduate Program (MSRI-UP)

5.1 Description of Undergraduate Program Please note: MSRI-UP is funded by an independent NSF grant, thus there is no report attached to Section 11 – Appendix.

Research Topic: Mathematical Finance Date: June 21, 2011 to July 24, 2011 Organizers: Ivelisse Rubio, Duane Cooper, Ricardo Cortez, Herbert Medina, Suzanne Weekes*

The MSRI-UP summer program was designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences. Due to funding restrictions, only U.S. citizens and permanent residents were eligible to apply and the program did accept foreign students regardless of funding. The academic portion of the 2011 program will be led by Dr. Marcel Blais.

General description During the summer, each of the 18 student participants:

* participated in the mathematics research program under the direction of Dr. Blais * completed a research project done in collaboration with other MSRI-UP students * gave a presentation and write a technical report on his/her research project * attended a series of colloquium talks given by leading researches in their fields * attended workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences and * learned techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships * received a $3000 stipend, lodging, meals and roundtrip travel to Berkeley, CA.

After the summer, each student:

* had an opportunity to attend a national mathematics or science conference where students will present their research * was part of a network of mentors that will provide continuous advice in the long term as the student makes progress in his/her studies * was contacted regarding future research opportunities

The main objective of the MSRI-UP is to identify talented students, especially those from underrepresented groups, who are interested in mathematics and make available to them meaningful research opportunities, the necessary skills and knowledge to participate in successful collaborations, and a community of academic peers and mentors who can advise, encourage and support them through a successful graduate program.

The objective is designed to contribute significantly toward meeting the program goal of increasing the number of graduate degrees in the mathematical sciences, especially doctorates, earned by U.S. citizens and permanent residents by cultivating heretofore untapped mathematical talent within the U.S. Black, Hispanic/Latino and Native American communities.

During the first two weeks of MSRI-UP, in preparation for their research, students will be introduced to several topics in mathematical finance, including special topics in probability and stochastic processes, arbitrage-free derivative pricing, the Black-Scholes-Merton partial differential equation, and liquidity models.During the remainder of the program, the students will work in teams on research projects.Below, we give examples of two research areas.

Project 1: Liquidity Modeling

In the fields of mathematical finance and financial engineering, a standard assumption is one of infinite liquidity of securities. Under this assumption all market agents are price takers, meaning that one can buy or sell any number of shares of a security instantaneously at the market price without affecting that market price. In reality, this assumption does not hold.One popular model which relaxes the assumption of infinite liquidity is presented by Cetin, Jarrow, and Protter . This model postulates the existence of a supply curve S_t(x) which gives the price of an asset as a function of trade size and is an extension of the standard Black-Scholes-Merton model. For highly liquid stocks, this curve has been found to be a linear function of trade size with a slope that changes randomly in time. For assets which are illiquid, the supply curve lacks this linear property but seems to have a piecewise-linear structure in trade size.Using financial data, students will investigate the supply curve for moderately liquid and illiquid assets and research methods for modeling the supply curve in these cases. Models will be tested statistically for goodness of fit using spline techniques, and the distribution of model parameters will be examined using tools from probability and stochastic processes.

Project 2: Cointegration and the Capital Asset Pricing Model

The ability to predict excess returns has been a goal of financial economists for decades. The Capital Asset Pricing Model (CAPM) is a commonly used factor model for predicting expected returns, but there are several unrealistic assumptions associated with this model that make the results unreliable, such as the assumption that supply equals demand for all assets and the assumption that investors act rationally when investing their money. This model also relies solely on how risky the asset in question is compared to the overall risk of the market portfolio when predicting returns. Fama and French improve the CAPM by incorporating additional risk factors into the model, but its predictive ability is still in question.Students will use the statistical technique of cointegration to to investigate long term relationships between macroeconomic factors, such as dividend yields and interest rates, and use these results to build factor models that expand on the CAPM and the Fama and French model. Financial data will be used to test the predictive power of the proposed factor models.

Short Biographies of the 2010 MSRI-UP organizers:

Suzanne Weekes is the Associate Professor and Associate Head of the Department of Mathematical Sciences at Worcester Polytechnic Institute (WPI) in Massachusetts. She received her PhD in Mathematics and Scientific Computing from the University of Michigan. At WPI, she is also the Director of the Center for Industrial Mathematics and Statistics CIMS. Prof. Weekes has been senior personnel, co-PI, or PI in the NSF-funded REU Program in Industrial Mathematics and Statistics at WPI for the last 11 years DMS 0097469, DMS 0353816, DMS 0649127, and DMS1004795. In this program, mathematics undergraduates do research on

56 problems that come straight from the various sectors of industry, and are of direct importance to the industrial partners and impact research and development at these companies. Her research interests are in numerical methods for PDES, spatio-temporal composites, fluid flow, and industrial mathematics and modeling.

She will be sharing this summer experience with her two young daughters who are looking forward to shedding their east coast ways and becoming California girls.

Ivelisse M. Rubio was born and raised in Puerto Rico. She received her B.S. and M.S. in Mathematics from the University of Puerto Rico-Río Piedras and her Ph.D. in Applied Mathematics from Cornell University. In 1998, she co-founded the NSF-REU Summer Institute in Mathematics for Undergraduates (SIMU) at the UPR-Humacao. Ive is currently a Professor in the Computer Science Department at the UPR-Rio Piedras. Her research interests are finite fields and applications to error-correcting codes.

Herbert A. Medina is a Professor of Mathematics at Loyola Marymount University. He completed his undergraduate studies at UCLA and Ph.D. at UC Berkeley. He is an analyst and has done work in Hilbert space operators (of a certain type) and some theoretical aspects of wavelets. He has also dabbled in other elementary math topics. Professor Medina has been involved in many undergraduate summer programs, including five summers as co-director of an REU at the University of Puerto Rico-Humacao.

5.2 MSRI-UP Data

Participants List

Participant Home Institution Arauza, Andrea California State University Belete, Nathan San Francisco State University Bello, Jason University of California Blizman, Allyson Joy Lycoming College Bongard, Michelle Marie Loyola Marymount University Burke, Kerisha Alecia Howard University LaBriola, Joseph Pomona College Lopez, Nathan Carl University of California Matovu, Daniel Quinton Illinois Institute of Technology Ochoa, Adrian Valles University of Arizona Osorio, Mike Diego Duke University Osorio, Jasmine Marie York College, CUNY Perkins, Raymond Morehouse College Pleasant, Kendra Enid North Carolina Agricultural and Technical State University Rosales, Elisa Renee University of Kansas Samaniego, Alejandro San Francisco State University David

Thaver, Vishnu Ranjan University of Notre Dame Thomas, Shayana M. Savannah State College

1. OVERVIEW OF ACTIVITIES 2011–12

1.1 Major Programs and their Associated Workshops

Note: The description of each activity is provided to MSRI by the organizers prior to the beginning of each activity; therefore, the verbs are in future tense. In the list of organizers of each activity, an asterisk (*) denotes lead organizer(s).

Program 1: Quantitative Geometry August 15, 2011 to December 16, 2011 Organized by Keith Ball (University College London, United Kingdom), Emmanuel Breuillard (Université Paris-Sud 11, France), Jeff Cheeger (New York University, Courant Institute), Marianna Csornyei (University College London, United Kingdom), Mikhail Gromov (Courant Institute and Institut des Hautes Études Scientifiques, France), Bruce Kleiner (New York University, Courant Institute), Vincent Lafforgue (Université Pierre et Marie Curie, France), Manor Mendel (The Open University of Israel), Assaf Naor* (New York University, Courant Institute), Yuval Peres (Microsoft Research Laboratories), and Terence Tao (University of California, Los Angeles)

The fall 2011 program "Quantitative Geometry" is devoted to the investigation of geometric questions in which quantitative/asymptotic considerations are inherent and necessary for the formulation of the problems being studied. Such topics arise naturally in a wide range of mathematical disciplines, with significant relevance both to the internal development of the respective fields, as well as to applications in areas such as theoretical computer science. Examples of areas that will be covered by the program are: geometric group theory, the theory of Lipschitz functions (e.g., Lipschitz extension problems and structural aspects such as quantitative differentiation), large scale and coarse geometry, embeddings of metric spaces and their applications to algorithm design, geometric aspects of harmonic analysis and probability, quantitative aspects of linear and non-linear Banach space theory, quantitative aspects of geometric measure theory and isoperimetry, and metric invariants arising from embedding theory and Riemannian geometry. The MSRI program aims to crystallize the interactions between researchers in various relevant fields who might have a lack of common language, even though they are working on related questions.

Workshops associated with the Quantitative Geometry Program:

Workshop 1: Connections for Women in Quantitative Geometry August 18, 2011 to August 19, 2011 Organized by Keith Ball* (University College London), Eva Kopecka (Mathematical Institute, Prague), Assaf Naor (Courant Institute), and Yuval Peres (Microsoft Research)

This workshop will provide an introduction to the program on Quantitative Geometry. There will be several short lecture series, given by speakers chosen for the accessibility of their lectures, designed to introduce non-specialists or students to some of the major themes of the program.

Workshop 2: Introductory Workshop on Quantitative Geometry August 22, 2011 to August 26, 2011 Organized by Keith Ball (University College London), Eva Kopecka* (Mathematical Institute, Prague), Assaf Naor (Courant Institute), and Yuval Peres (Microsoft Research)

Quantitative Geometry deals with geometric questions in which quantitative or asymptotic considerations occur. The workshop will provide a mathematical introduction, a foretaste, of the many themes this exciting topic comprises: geometric group theory, theory of Lipschitz functions, large scale and coarse geometry, embeddings of metric spaces, quantitative aspects of Banach space theory, geometric measure theory and of isoperimetry, and more.

Workshop 3: Probabilistic Reasoning in Quantitative Geometry September 19, 2011 to September 23, 2011 Organized by Anna Erschler* (Université Paris-Sud), Assaf Naor (Courant Institute), and Yuval Peres (Microsoft Research)

"Probabilistic Reasoning in Quantitative Geometry" refers to the use of probabilistic techniques to prove geometric theorems that do not have any a priori probabilistic content. A classical instance of this approach is the probabilistic method to prove existence of geometric objects (examples include Dvoretzky's theorem, the Johnson- Lindenstrauss lemma, and the use of expanders and random graphs for geometric constructions). Other examples are the use of probabilistic geometric invariants in the local theory of Banach spaces (sums of independent random variables in the context of type and cotype, and martingale-based invariants), the more recent use of such invariants in metric geometry (e.g., Markov type in the context of embedding and extension problems), probabilistic tools in group theory, the use of probabilistic methods to prove geometric inequalities (e.g., maximal inequalities, singular integrals, Grothendieck inequalities), the use of probabilistic reasoning to prove metric embedding results such as Bourgain's embedding theorem (where the embedding is deterministic, but its analysis benefits from a probabilistic interpretation), probabilistic interpretations of curvature and their applications, and the use of probabilistic arguments in the context of isoperimetric problems (e.g., Gaussian, rearrangement, and transportation cost methods).

Workshop 4: Embedding Problems in Banach Spaces and Group Theory October 17, 2011 to October 21, 2011 Organized by William Johnson* (Texas A&M University), Bruce Kleiner (Yale University and Courant Institute), Gideon Schechtman (Weizmann Institute), Nicole Tomczak- Jaegermann (University of Alberta), and Alain Valette (Université de Neuchâtel)

This workshop is devoted to various kinds of embeddings of metric spaces into Banach spaces, including biLipschitz embeddings, uniform embeddings, and coarse embeddings, as well as linear embeddings of finite dimensional spaces into low dimensional spaces. There will be an emphasis on the relevance to geometric group theory, and an exploration into the use of metric differentiation theory to effect embeddings.

Workshop 5: Quantitative Geometry in Computer Science December 5, 2011 to December 9, 2011 Organized by Irit Dinur (Weizmann Institute), Subhash Khot (Courant Institute), Manor Mendel* (Open University of Israel and Microsoft Research), Assaf Naor (Courant Institute), and Alistair Sinclair (University of California, Berkeley)

Geometric problems which are inherently quantitative occur in various aspects of theoretical computer science, including: a) algorithmic tasks for geometric questions such as clustering and proximity data structures, b) geometric methods in the design of approximation algorithms for combinatorial optimization problems, including the analysis of semidefinite programs and embedding methods, c) and geometric questions arising from computational complexity, particularly in hardness of approximation. These include isoperimetric and Fourier analytic problems. These include isoperimetric and Fourier analytic problems.

This workshops aims to present recent progress in these directions.

Program 2: Random Spatial Processes January 9, 2012 to May 18, 2012 Organized by Mireille Bousquet-Mélou (Université de Bordeaux I, France), Richard Kenyon* (Brown University), Greg Lawler (University of Chicago), Andrei Okounkov (Columbia University), and Yuval Peres (Microsoft Research Laboratories)

In recent years probability theory (and here we mean probability theory in the largest sense, comprising combinatorics, statistical mechanics, algorithms, simulation) has made immense progress in understanding the basic two-dimensional models of statistical mechanics and random surfaces. Prior to the 1990s the major interests and achievements of probability theory were (with some exceptions for dimensions 4 or more) with respect to one-dimensional objects: Brownian motion and stochastic processes, random trees, and the like. Inspired by work of physicists in the ’70s and ’80s on conformal invariance and field theories in two dimensions, a number of leading probabilists and combinatorialists began thinking about spatial process in two dimensions: percolation, polymers, dimer models, Ising models. Major breakthroughs by Kenyon, Schramm, Lawler, Werner, Smirnov, Sheffield, and others led to a rigorous underpinning of conformal invariance in two-dimensional systems and paved the way for a new era of “two-dimensional” probability theory.

Workshops associated with the Random Spatial Processes Program:

Workshop 1: Connections for Women: Discrete Lattice Models in Mathematics, Physics, and Computing January 12, 2012 to January 13, 2012

61 Organized by Beatrice de Tiliere (University Pierre et Marie Curie), Dana Randall* (Georgia Institute of Technology), and Chris Soteros (University of Saskatchewan)

This 2-day workshop will bring together researchers from discrete mathematics, probability theory, theoretical computer science and statistical physics to explore topics at their interface. The focus will be on combinatorial structures, probabilistic algorithms and models that arise in the study of physical systems. This will include the study of phase transitions, probabilistic combinatorics, Markov chain Monte Carlo methods, and random structures and randomized algorithms.

Since discrete lattice models stand at the interface of these fields, the workshop will start with background talks in each of the following three areas: Statistical and mathematical physics; Combinatorics of lattice models; Sampling and computational issues. These talks will describe the general framework and recent developments in the field and will be followed with shorter talks highlighting recent research in the area.

The workshop will celebrate academic and gender diversity, bringing together women and men at junior and senior levels of their careers from mathematics, physics and computer science.

Workshop 2: Introductory Workshop: Lattice Models and Combinatorics January 16, 2012 to January 20, 2012 Organized by Cédric Boutillier (Université Pierre et Marie Curie), Tony Guttmann* (University of Melbourne), Christian Krattenthaler (University of Vienna), Nicolai Reshetikhin (University of California, Berkeley), and David Wilson (Microsoft Research)

Research at the interface of lattice statistical mechanics and combinatorial problems of “large sets” has been and exciting and fruitful field in the last decade or so. In this workshop we plan to develop a broad spectrum of methods and applications, spanning the spectrum from theoretical developments to the numerical end. This will cover the behaviour of lattice models at a macroscopic level (scaling limits at criticality and their connection with SLE) and also at a microscopic level (combinatorial and algebraic structures), as well as efficient enumeration techniques and Monte Carlo algorithms to generate these objects.

Workshop 3: Percolation and Interacting Systems February 20, 2012 to February 24, 2012 Organized by Geoffrey R. Grimmett (University of Cambridge), Eyal Lubetzky* (Microsoft Research), Jeffrey Steif (Chalmers University of Technology), and Maria E. Vares (Centro Brasileiro de Pesquisas Físicas)

Over the last ten years there has been spectacular progress in the understanding of geometrical properties of random processes. Of particular importance in the study of these complex random systems is the aspect of their phase transition (in the wide sense of an abrupt change in macroscopic behavior caused by a small variation in some

62 parameter) and critical phenomena, whose applications range from physics, to the performance of algorithms on networks, to the survival of a biological species.

Recent advances in the scope of rigorous scaling limits for discrete random systems, most notably for 2D systems such as percolation and the Ising model via SLE, have greatly contributed to the understanding of both the critical geometry of these systems and the behavior of dynamical stochastic processes modeling their evolution. While some of the techniques used in the analysis of these systems are model-specific, there is a remarkable interplay between them. The deep connection between percolation and interacting particle systems such as the Ising and Potts models has allowed one model to successfully draw tools and rigorous theory from the other.

The aim of this workshop is to share and attempt to push forward the state-of-the-art understanding of the geometry and dynamic evolution of these models, with a main focus on percolation, the random cluster model, Ising and other interacting particle systems on lattices.

Workshop 4: Statistical Mechanics and Conformal Invariance March 26, 2012 to March 30, 2012 Organized by Philippe Di Francesco* (Commissariat à Énergie Atomique, CEA), Andrei Okounkov (Columbia University), Steffen Rohde (University of Washington ), and Scott Sheffield (Massachusetts Institute of Technology, MIT)

Our understanding of the scaling limits of discrete statistical systems has shifted in recent years from the physicists' field-theoretical approaches to the more rigorous realm of probability theory and complex analysis. The aim of this workshop is to combine both discrete and continuous approaches, as well as the statistical physics/combinatorial and the probabilistic points of view. Topics include quantum gravity, planar maps, discrete conformal analysis, SLE, and other statistical models such as loop gases.

Workshop 5: Random Walks and Random Media April 30, 2012 to May 4, 2012 Organized by Noam Berger (The Hebrew University of Jerusalem), Nina Gantert (Technical University, Munich), Andrea Montanari (Stanford University), Alain-Sol Sznitman (Swiss Federal Institute of Technology, ETH Zurich), and Ofer Zeitouni* (University of Minnesota/Weizmann Institute)

The field of random media has been the object of intensive mathematical research over the last thirty years. It covers a variety of models, mainly from condensed matter physics, physical chemistry, and geology, where one is interested in materials which have defects or inhomogeneities. These features are taken into account by letting the medium be random. It has been found that this randomness can cause very unexpected effects in the large scale behavior of these models; on occasion these run contrary to the prevailing intuition. A feature of this area, which it has in common with other areas of statistical physics, is that what was initially thought to be just a simple toy model has turned out to be a major mathematical challenge.

Program 3: Complementary Program August 15, 2011 to May 18, 2012

MSRI had a small Complementary Program comprised of two postdoctoral fellows, Fatemeh Mohammadi from Ferdowsi University of Mashhad and Thomas Mettler from University of Fribourg and two research members, Susanna Fishel from Arizona State University and Esther Lamken from Center for Communications Research, La Jolla.

1.2 Scientific Activities Directed at Underrepresented Groups in Mathematics

Undergraduate Program: MSRI-UP 2012: Enumerative Combinatorics June 16, 2012 to July 29, 2012 Organized by Duane Cooper (Morehouse College), Ricardo Cortez (Tulane University), Herbert Medina (Loyola Marymount University), Ivelisse Rubio (University of Puerto Rico, Rio Piedras Campus), and Suzanne Weekes* (Worcester Polytechnic Institute)

During the first two weeks of MSRI-UP, in preparation for their research, students will be introduced to several topics in enumerative combinatorics, including Möbius functions, partially-ordered sets, polyhedra, lattice-point enumeration, hyperplane arrangements, and various graph polynomials. During the remainder of the program, the students will work in teams on research projects. Below we give examples of two research projects.

Project 1: Graceful Labellings

A graceful labelling of a graph G=(V,E) is an assignment of the vertices with distinct labels from 1 to |V| such that the absolute values of the differences of labels of adjacent vertices are the numbers 1 to |E|. A major conjecture in graph theory suggests that every tree has a graceful labelling. Study a less restrictive problem: namely, given a integer paramenter k, how many weakly graceful labellings are there of size k? Here a weakly graceful labelling of size k means that we assign (not necessarily distinct) labels from 1 to k in such a way that the absolute values of the differences of labels of adjacent vertices are distinct. This problem can be tackled from the viepoint of inside-out polytopes.

Project 2: Ehrhart Series Decompositions for Rational Polytopes

The Ehrhart polynomial of a lattice polytope P (the convex hull of a finite number of points in Z^d) counts the number of integer lattice points in integer dilates of P. The Ehrhart series is the generating function of the Ehrhart polynomial (and thus encodes the same information). Ehrhart's theorem says that if P is a lattice polytope then its Ehrhart series is of the form h(z)/(1-z)^{d+1} for some polynomial h(z). Alan Stapledon (http://arxiv.org/abs/0904.3035) used a decomposition of h(z) into two palindromic polynomials and proved inequalities for their coefficients, which in turn implied (known, famous) inequalities on the coefficients of h(z). If P is rational (i.e., a convex hull of points in Q^d) then its Ehrhart series can be written as h(z)/(1-z^p)^{d+1} for some p. Find and study a Stapledon-like decomposition of h(z) in this rational case. A first pointer

64 could be Matthew Fiset and Alexander Kasprzyk's paper [Electronic Journal of Combinatorics 15(1), 2008, Note 18].

Workshop 1: Mathematics Institutes' Modern Math (SACNAS) October 26, 2011 to October 27, 2011 Organized by Ricardo Cortez (Tulane University), Suzanne Lenhart (University of Tennessee), Christian Ratsch (Institute for Pure and Applied Mathematics, Associate Director), and Ivelisse Rubio (University of Puerto Rico, Computer Science)

The eight NSF mathematics institutes are pleased to offer three concurrent sessions immediately preceding the SACNAS annual meeting – one for graduate students and recent PhDs, and two for undergraduate students – to invigorate the research careers of minority mathematicians and mathematics faculty at minority-serving institutions. The “Modern Math Workshop” will highlight presentations on topics drawn from the institutes’ upcoming programs, a keynote speaker, and an informative panel presentation on the 2012-13 programs and workshops. The two undergraduate sessions (applicants will choose one) are appropriate for students of any major interested in learning how mathematics contributes to our understanding of various scientific topics. Activities will include lectures and group work.

All sessions will begin with lunch on Wed. Oct. 26 and include an evening reception. The sessions will continue on Thursday morning and will end at 12:30 pm prior to the SACNAS conference lunch. The three sessions will combine for the keynote lecture by Mariel Vazquez.

“Modern Math Workshop” (for graduate students and recent PhDs): The workshop features 40-minute presentations by eight speakers, one on behalf of each institute. The speakers are typically chosen from among the organizers of upcoming programs at those institutes and are expected to give an accessible presentation on exciting and current research topics associated with the upcoming institute programs. In addition there will be an informational panel of institute representatives, which will describe upcoming programs and other opportunities offered by the institutes and how to participate in them.

There will also be a keynote lecture “DNA Unknotting and Unlinking” by Mariel Vazquez on Wednesday afternoon. Mariel Vazquez is an Associate Professor at San Francisco State University. Her current research focuses on the applications of topological and discrete methods to the study of DNA, with emphasis on the topological changes affected by enzymes such as topoisomerases and site-specific recombinases.

“Undergraduate Minicourses in Mathematics”: Two minicourses for an undergraduate audience will be offered at the same time as the Modern Math Workshop. Applicants will choose one of the following.

1) Suzanne Lenhart: Optimal Control of Ordinary Differential Equations

65 Suzanne Lenhart, whose main research area is optimal control applied to biological models, will present introductory material on optimal control for ordinary differential equations. The basic idea is to find optimal 'controls' (types of coefficients or source terms) in ordinary differential equations to achieve a goal (like minimizing infecteds in a disease model). After giving some background on the theory and basic techniques, students will be asked to solve a simple problem in groups and to formulate a more complicated problem for a model of their own interest. The course will also include demonstrations of examples using user-friendly MATLAB codes. Suzanne Lenhart is a mathematics professor at U of Tennessee and is the Associate Director for Education, Outreach and Diversity at the National Institute for Mathematical and Biological Synthesis.

2) Federico Ardila: Counting Lattice Points in Polytopes A polytope is the higher-dimensional generalization of a polygon. After discussing some of the basic facts about them, we will study the problem of "measuring" a polytope by counting the lattice points inside it. This problem arises very naturally in several areas of mathematics, and it leads to some beautiful combinatorics. Federico Ardila is an assistant professor at San Francisco State University and an adjunct professor at the Universidad de Los Andes in Bogotá. His research studies objects in algebra, geometry, topology, and applications by understanding their underlying combinatorial structure. He leads the SFSU–Colombia Combinatorics Initiative, a research and learning collaboration between students in the United States and Colombia.

Workshop 2: Spring Opportunities March 12, 2012 to March 14, 2012 Organized by Dave Auckly (MSRI)

Mathematics is becoming increasingly important for addressing many of the critical economic, environmental, and human health related challenges that our nation is currently facing. Therefore, the education and training of a diverse mathematical workforce capable of boldly developing new mathematical theories and profoundly understanding eminent scientific discoveries is of the highest national priority.

This new series of workshops is designed to cultivate a diverse community of existing and aspiring mathematical scientists to meet this challenge. The overall goal of the series is to familiarize people who have not been well represented in the mathematical sciences with professional opportunities in academia, industry, and government; as well as to help young researchers find jobs and mentors within the profession through networking. This first workshop in the series addresses the professional advancement of underrepresented minorities in the mathematical sciences. It will also include an introduction to mathematics represented in the MSRI research programs aimed at faculty in minority serving and primarily undergraduate institutions. Anyone who will be seeing employment in mathematics within the next couple of years would benefit from attending this workshop.

66 Workshop 3: Infinite Possibilities Conference 2012 March 30, 2012 to March 31, 2012 Organized by Jacqueline Akinpelu (The Johns Hopkins University, Applied Physics Lab), Leona Harris (The College of New Jersey), Gayle Herrington (Columbus State University), Raegan Higgins (Texas Tech University), Fern Hunt (National Institute of Standards and Technology), Karen Ivy (New Jersey City University), Lily Khadjavi* (Loyola Marymount University), Dawn Lott (Delaware State University), Tanya Moore (Building Diversity in Science), Rehana Patel (Wesleyan University), Nagambal Shah (Spelman College), Kim Weems (North Carolina State University), Cristina Villalobos (University of Texas-Pan American), Sue Minkoff (University of Maryland, Baltimore County), Nagaraj Neerchal (University of Maryland, Baltimore County), Janet Rutledge (University of Maryland, Baltimore County), Renetta Tull (University of Maryland, Baltimore County), Yi Huang (University of Maryland, Baltimore County), DoHwan Park (University of Maryland, Baltimore County), Manil Suri (University of Maryland, Baltimore County), and John Zweck (University of Maryland, Baltimore County)

The Infinite Possibilities Conference (IPC) is a national conference that is designed to promote, educate, encourage and support minority women interested in mathematics and statistics.

2005 IPC: Spelman College; Atlanta, GA. 2007 IPC: Building Diversity in Science, North Carolina State University and Statistical and Applied Mathematical Sciences Institute; Raleigh, NC. 2010 IPC: Building Diversity in Science, Institute of Pure and Applied Mathematics, University of California, Los Angeles; Los Angeles, CA. 2012 IPC: Building Diversity in Science and University of Maryland, Baltimore County. Baltimore, MD.

African-American, Hispanic/Latina, and American Indian women have been historically underrepresented in mathematics. In 2002, less than 1% of the doctoral degrees in the mathematical sciences were awarded to American women from underrepresented minority groups. Even professionals who have succeeded in completing advanced degree programs in science and engineering fields can face inequities within their professional lives with respect to advancement and salaries. What is being envisioned through this conference is that in order to increase and support diversity in the mathematics community, a paradigm shift needs to occur in the way we think about the image of a mathematician and about the role a mathematician plays in society. Although some workshops and conferences have been created to address race/ethnicity or gender in the context of mathematics, no conference or program has been specially designed to address both.

Highlights of conference activities include: Professional development workshop series; Panel discussion on graduate studies in mathematics; Research talks given by professionals; Student poster sessions, Special activities for high school students; Roundtable discussions on experiences with mathematics; Awards banquet in honor of Dr. Etta Z. Falconer that will highlight special achievements in mathematics.

1.3 Summer Graduate Schools 2011

SGS 1: Commutative Algebra June 6, 2011 to June 17, 2011 Organized by Daniel Erman (Stanford University), Irena Swanson* (Reed College), and Amelia Taylor (Colorado College)

This workshop will involve a combination of theory and symbolic computation in commutative algebra. The lectures are intended to introduce three active areas of research: Boij-Söderberg theory, algebraic statistics, and integral closure. The lectures will be accompanied with tutorials on the computer algebra system Macaulay 2.

SGS 2: The Dirichlet Space: Connections between Operator Theory, Function Theory, and Complex Analysis June 20, 2011 to July 1, 2011 Organized by Nicola Arcozzi (Universita\' di Bologna), Richard Rochberg (Washington University), Eric T Sawyer (McMaster University), Brett D Wick* (Georgia Institute of Technology)

This workshop will focus on the classical Dirichlet space of holomorphic functions on the unit disk. This space is at the center of several active, interrelated areas of research that, viewed more broadly, focus on the interaction between function theoretic operator theory and potential theory. There are several goals of this Summer Graduate Workshop. First, mathematically, the workshop will demonstrate the basic properties of the Dirichlet space, then introduce the technique of Trees in Function Spaces. The workshop will show the interconnections between the areas of Complex Analysis, Function Theory, and Operator Theory and will also illustrate the real-variable analogues of the analytic result discussed.

SGS 3: IAS-PCMI Summer School on Moduli Spaces of Riemann Surfaces Location: Salt Lake City, Utah July 3, 2011 to July 23, 2011 Organized by Benson Farb (University of Chicago), Richard Hain (Duke University), and Eduard Looijenga (University of Utrecht, Netherlands)

This workshop takes place at the Institute for Advanced Study – Park City Mathematics Institute and is reported independently by the organizers.

The study of moduli spaces of Riemann surface is a rich mixture of geometric topology, algebraic topology, complex analysis and algebraic geometry. Each community of researchers that studies these moduli spaces generates its own problems and its own techniques for solving them. However, it is not uncommon for researchers in one community to solve problems generated by another once they become aware of them. The goal of this summer school is to give graduate students a broad background in the various approaches to the study of moduli spaces of Riemann surfaces so that they will be

68 aware of the problems and techniques of many of the communities that study these fascinating objects. Graduate student participants from the various communities will be encouraged to interact with their colleagues from the other communities of students in order to maximize cross fertilization.

SGS 4: Geometric Measure Theory and Applications July 11, 2011 to July 22, 2011 Organized by Camillo De Lellis (Universität Zürich), Tatiana Toro* (University of Washington)

Geometric Measure Theory (GMT) is a field of Mathematics that has contributed greatly to the development of the calculus of variations and geometric analysis. In recent years it has experienced a new boom with the development of GMT in the metric space setting which has led to unexpected applications (for examples to questions arising from theoretical computer sciences). The goal of this summer graduate workshop is to introduce students to different aspects of this field. There will be 5 mini-courses and a couple of research lectures. We expect students to have a solid background in measure theory.

SGS 5: Toric Varieties Location: Cortona, Italy July 18, 2011 to July 29, 2011 Organized by David Cox* (Amherst College), Hal Schenck (University of Illinois), Giorgio Patrizio (Università di Firenze, Italy), and Sandro Verra (Università di Roma Tre, Italy)

Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by glueing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

SGS 6: Cluster Algebras and Cluster Combinatorics August 1, 2011 to August 12, 2011 Organized by Gregg Musiker (University of Minnesota), Lauren Williams* (University of California, Berkeley)

Cluster algebras are a class of combinatorially defined rings that provide a unifying structure for phenomena in a variety of algebraic and geometric contexts. A partial list of related areas includes quiver representations, statistical physics, and Teichmuller theory. This summer workshop for graduate students will focus on the combinatorial aspects of cluster algebras, thereby providing a concrete introduction to this rapidly-growing field. Besides providing background on the fundamentals of cluster theory, the summer school will cover complementary topics such as total positivity, the polyhedral geometry of

69 cluster complexes, cluster algebras from surfaces, and connections to statistical physics. No prior knowledge of cluster algebras will be assumed.

The workshop will consist of four mini-courses with accompanying tutorials. Students will also have opportunities for further exploration using computer packages in Java and Sage.

SGS 7: Séminaire de Mathématiques Supérieures 2011. Metric Measure Spaces: Geometric and Analytic Aspects Location: Montreal, Canada June 27, 2011 to July 8, 2011 Organized by Galia Dafni* (Concordia University, Montreal), Robert McCann (University of Toronto), and Alina Stancu (Concordia University, Montreal)

In recent decades, metric-measure spaces have emerged as a fruitful source of mathematical questions in their own right, and as indispensable tools for addressing classical problems in geometry, topology, dynamical systems and partial differential equations. The purpose of the 2011 summer school is to lead young scientists to the research frontier concerning the analysis and geometry of metric-measure spaces, by exposing them to a series of mini-courses featuring leading researchers who will present both the state-of-the-art and the exciting challenges which remain.

1.4 Other Scientific Workshops

Workshop 1: Chern Centennial Conference October 30, 2011 to November 4, 2011 Organized by Robert Bryant (Co-Chair, Mathematical Science Research Institute - MSRI), Yiming Long (Co-Chair, Chern Institute of Mathematics - CIM), Hélène Barcelo (Mathematical Science Research Institute - MSRI), May Chu (S. S. Chern Foundation for Mathematical Research), and Lei Fu (Chern Institute of Mathematics - CIM)

The Mathematical Sciences Research Institute (MSRI), in conjunction with the Chern Institute of Mathematics (CIM) in Tianjin, China, celebrates the centennial of the birth of Shiing-Shen Chern, one of the greatest geometers of the 20th century and MSRI's co- founder. In commemoration of Chern's work, MSRI and CIM will hold a two-week international mathematics conference. During the first week, October 24 to 28, 2011, the conference will take place at CIM in Tianjin, China. During the second week, October 30 to November 5, 2011, the conference will be held at MSRI in Berkeley, California.

Workshop 2: Bay Area Differential Geometry Seminar (BADGS) 2011-12 Location: Berkeley and Stanford, California November 19, 2011 and February 4, 2012 to February 5, 2012 Organized by David Bao (San Francisco State University), Robert Bryant (Mathematical Sciences Research Institute), Joel Hass (University of California, Davis), David Hoffman* (Stanford University), Rafe Mazzeo (Stanford University), and Richard Montgomery (University of California, Santa Cruz)

The Bay Area Differential Geometry Seminar meets three times per year and is a one-day seminar on recent developments in differential geometry and geometric analysis, broadly interpreted. Typically, it runs from mid-morning until late afternoon with three to four speakers. Lunch will be available at MSRI (participants will be asked to make a donation to help defray their lunch expenses), and the final talk will be followed by dinner.

Workshop 3: Hot Topics: Thin Groups and Super-strong Approximation February 6, 2012 to February 10, 2012 Organized by Emmanuel Breuillard* (Universite Paris-Sud, Orsay), Alexander Gamburd (CUNY Graduate Center), Jordan Ellenberg (University of Wisconsin - Madison), Emmanuel Kowalski (ETH Zurich), Hee Oh (Brown University)

The workshop will focus on recent developments concerning various quantitative aspects of "thin groups". These are discrete subgroups of semisimple Lie groups which are both « big » (i.e. Zariski dense) and « small » (i.e. of infinite co-volume). This dual nature leads to many intricate questions. Over the past few years, many new ideas and techniques, arising in particular from arithmetic combinatorics, have been involved in the study of such groups, leading for instance to far-reaching generalizations of the strong approximation theorem in which congruence quotients are shown to exhibit a spectral gap (super-strong approximation).

Simultaneously and sometimes surprisingly, the study of thin groups turns out to be of fundamental importance in a variety of subjects, including equidistribution of homogeneous flows and lattice points counting problems, dynamics on Teichmuller space, the Bourgain-Gamburd-Sarnak sieve in orbit, and arithmetic or geometric properties of certain types of monodromy groups and coverings. The workshop will gather a variety of experts from group theory, number theory, ergodic theory and harmonic analysis to present the accomplishments to date to a broad audience and discuss directions for further study.

1.5 Educational & Outreach Workshops

Workshop 1: Bay Area Circle for Teachers Summer 2011 June 20, 2011 to June 24, 2011 Organized by Dave Auckly (MSRI)

The core of the summer workshop will consist of the morning and afternoon sessions held from Monday through Friday. This time will be devoted to discovery, problem solving, and interactive learning. During the earlier part of the week teachers will gain experience with a variety of problem solving techniques such as symmetry, mathematical patterns, and parity. Subsequent sessions will focus on particular topics such as geometry, sequences, counting, and number theory. Traditionally relegated to the high school curriculum or beyond, these topics actually provide a natural starting point for exploring and appreciating interesting mathematics at the middle school level. All the sessions will be led by exceptional educators and mathematicians from the San Francisco Bay area.

71 We are grateful to the Firedoll, Simons and Bechtel Foundations as well as MSRI for supporting our summer instructors.

A major theme throughout the week will be finding creative answers to the question of how to incorporate a problem-solving approach to math education into the existing curriculum. To this end leaders will supply participants with handouts or short modules based on the material covered during their sessions. They will also work with teachers to share ideas for enlivening any math class and to develop lesson plans. Focused discussions will be held regularly to determine what obstacles exist to incorporating this style of teaching into the present curriculum, what resources would be most helpful to teachers, and other related topics.

Workshop 2: Bay Area Circle for Teachers Spring 2012 January 28, 2012 Organized by Dave Auckly (MSRI)

The Winter workshop supports teachers in their development of problem solving skills as well as sharing with them information about upcoming mathematical opportunities for students and teachers. This will be a great opportunity for teachers new to the Math Circle program as well as experienced Math Circle teachers.

Workshop 3: Summer Institute for the Professional Development of Middle School Teachers 2011 (Wu Summer Institute) July 25, 2011 to August 12, 2011 Organized by Hung-Hsi Wu (University of California, Berkeley)

This is a three-week institute (July 25 to August, 2011) on whole numbers and fractions together with five Saturday sessions spread over the 2011-2012 school year. The main target is upper elementary school teachers from the Bay Area; preference will be given to teams from the same school or same district. However, middle and high school teachers will also be considered. There is a limited number of seats, so get your application in as soon as possible.

Participating teachers will each receive a stipend of $100 for each full day of attendance. Please note, however, that excessive absences may result in being dropped from the institute.

This institute is devoted specifically to the content knowledge needed for teaching grades K--6. It will not discuss advanced topics or fun topics that are divorced from the school classroom, nor will it discuss topics germane to grades K--6 by using sophisticated methods that are inappropriate for K--6. At the same time, it will not be concerned with classroom projects that you can immediately put to use to enrich your next lesson. This is not a strategies workshop. Instead, it takes a long-term view that, for you to become a teacher who can implement the Common Core Standards, you have to achieve a better command of the mathematics you teach. You need both a coherent global view of the bread and butter topics of K--6, whole numbers and fractions, as well as a robust

72 understanding of the inner details. Unfortunately, such knowledge seems to be in short supply at present, and the purpose of the institute is to fill in this gap.

Five days of the institute will be devoted to the basics of whole numbers, with emphasis on how to count in the decimal system, the use of the number line, standard algorithms, and the how and why of estimations. Four days will be on elementary number theory: divisibility rules, greatest common factor, and prime factorization. The last six days will cover the definition of fractions and their arithmetic operations. The tentative plan is to follow this institute with institutes on pre-algebra and algebra in the next two years that will help teachers negotiate the Common Core Standards of grades 6--8.

Each of the 15 weekdays of the institute will begin promptly at 8:30 am and end at 4:30 pm. There will be a total of five hours of lecture and seat work (with breaks and lunch); the lectures will be on mathematics. (Material on which the lectures are based will be handed out during the first days.) Two hours of small group discussions at the end of the day will be given over to discussions of pedagogy or the homework assignment of the day before. There will be homework assignments every day.

The institute assumes a willingness to work, perhaps even intensely, during the three- week period. With this in mind, we ask that you make a commitment to the following:

Attend all fifteen days of the institute and the five follow-up Saturday sessions during the 2011-2012 school year. In particular, no stipend will be given to partial attendance of the fifteen-day institute unless there is a medical reason. Do the daily homework assignments. Be willing to learn and to participate in discussions.

Workshop 4: Critical Issues in Mathematics Education 2012: Teacher education in view of the Common Core March 21, 2012 to March 23, 2012 Organized by Dave Auckly (MSRI), Hyman Bass (University of Michigan), Amy Cohen- Corwin (Rutgers University), and William McCallum (University of Arizona)

The wide adoption of the Common Core State Standards for Mathematics (CCSSM) offers a helpful curricular coherence to the environment of teacher education. And so the CCSSM present both an opportunity and a challenge to teacher education. An opportunity because of the greater focus made possible. A challenge because not only of the ambitious level of the CCSSM, but also of the prominent role in them of Mathematical Practices. While most mathematicians will find these congenial, much needs to be done to make them meaningfully understood by teachers and teacher educators, and, still more, how to enact them as an organic aspect of instruction. The CIME workshop aims to gather and stimulate ideas for how to meet this opportunity and challenge.

73 Workshop 5: Circle on the Road at MAA MathFest 2011 Location: Lexington, Kentucky August 3, 2011 to August 6, 2011 Organized by Dave Auckly (MSRI)

The annual summer meeting of the Mathematical Association of America is the premier summertime event in mathematics. The meeting offers a substantial mathematical program that promises to be fascinating, informative, and productive. In keeping with the less formal summer season there are also many opportunities to enjoy mathematics and to have fun with it.

Workshop 6: Circle on the Road at Joint Math Meetings 2012 Location: Boston, Massachusetts January 4, 2012 to January 7, 2012 Organized by Dave Auckly (MSRI)

The Joint Mathematics Meetings comes to New England! The Mathematical Association of America (MAA) and the American Mathematical Society (AMS) invite you to join them at the next Joint Mathematics Meetings which will be held in Boston, known not only for its rich history but also for its central location to many colleges and universities. This will be the 95th annual winter meeting of MAA and the 118th annual meeting of AMS. The Joint Mathematics Meetings will again host sessions by the Association for Symbolic Logic, the Association for Women in Mathematics, the National Association for Mathematicians, and the Society for Industrial and Applied Mathematics.

Look for a few Joint Mathematics Meetings' mainstays such as

a comprehensive and rich scientific program geared toward mathematicians of all ages and levels of expertise; recognition of numerous mathematical achievements through Prize and Award Ceremonies; courses such as the MAA Short Course, two AMS Short Courses, and the MAA Minicourses; many activities for students such as the Graduate School Fair for undergraduate students; poster sessions for young mathematicians and undergraduate students; employment opportunities at the Mathematical Sciences Employment Center; the Mathematical Art Exhibition that includes works by artists in various media; the Who Wants to Be a Mathematician Competition that showcases the brilliance of ten of the nation's best high school math students; exhibits filled with some of the leading scientific publishers, well-known computer hardware and software manufacturers, well-known health and lifestyle companies, companies offering mathematics enrichment products, and professional organizations

74 Workshop 7: Circle on the Road Spring 2012 April 13, 2012 to April 15, 2012 Organized by Dave Auckly (MSRI), Robert Sachs, Amanda Serenevy, Dan Ullman

This workshop will bring together new and experienced leaders of math circles for students and teachers. We welcome anyone who is interested in learning more about math circles, especially teachers.

Workshop activities will include discussions, presentations, and a mathematics festival to be held outside of the MathAlive! exhibit that will be in the Smithsonian Institution.

Participants will begin collaborating before the workshop to develop sample math circle sessions that they will present during the festival. These activities will be collaboratively evaluated and refined during the workshop.

75 2. 2011-12 PROGRAM AND WORKSHOP PARTICIPANT SUMMARY

Time Activity Type Activity Title No. of Participants MSRI Postdocs PD/RMs Ambrus, Gergely Azzam, Jonas Aziz Le Donne, Enrico Meyerson, William Paul Nelson, Jelani O Nowak, Piotr Peng, Irine Srivastava, Nikhil Thompson, Russ Michael Wang, Lu Wang, Yi Wang, Zhiren Williams, Marshall Fall 2011 Scientific Program Quantitative Geometry 89 Yin, Qian Israel, Arie Connections for Women: Quantitative 08/18/11 to 08/19/11 Programmatic Workshop Geometry 45 Introductory Workshop on Quantitative 08/22/11 to 08/26/11 Programmatic Workshop Geometry 89 Probabilistic Reasoning in Quantitative 09/19/11 to 09/23/11 Programmatic Workshop Geometry 71 Embedding Problems in Banach Spaces and 10/17/11 to 10/21/11 Programmatic Workshop Group Theory 69

12/05/11 to 12/09/11 Programmatic Workshop Quantitative Geometry in Computer Science 49

Ahlberg, Daniel Bettinelli, Jeremie L Chhita, Sunil Ding, Jian Drenning, Shawn - Viterbi Fang, Ming Gorin, Vadim Kargin, Vladislav Levit, Anna Mkrtchyan, Sevak Shkolnikov, Mykhaylo Sousi, Perla Spring 2012 Scientific Program Random Spatial Processes 78 Young, Benjamin J Panova, Greta Connection for Women in Random Spatial Processes (Discrete Lattice Models in 01/11/12 to 01/13/12 Programmatic Workshop mathematics, physics, and computing) 66 Introductory Workshop: Lattice Models and 01/16/12 to 01/20/12 Programmatic Workshop Combinatorics 114 02/20/12 to 02/24/12 Programmatic Workshop Random Graphs and Percolation 93 Statistical Mechanics and Conformal 03/26/12 to 03/30/12 Programmatic Workshop Invariance 92 04/30/12 to 05/04/12 Programmatic Workshop Random Walks and Random Media has not occurred yet

Mettler, Thomas Whole Year 2011-12 Scientific Program Complementary Program 2011-12 4 Mohammadi, Fatemeh

Scientific Activities Directed at Underrepresented Groups in 06/16/12 to 07/29/12 Mathematics MSRI-UP 2012: Undergraduate Program has not occurred yet Scientific Activities Directed at Underrepresented Groups in Mathematics Institutes' Modern Math 10/26/11 to 10/27/11 Mathematics Workshop (SACNAS) approx. 250 Scientific Activities Directed at Underrepresented Groups in 03/12/12 to 03/14/12 Mathematics Spring Opportunities 52 Scientific Activities Directed at Underrepresented Groups in 03/30/12 to 03/31/12 Mathematics Infinite Possibilities approx. 150

06/06/11 to 06/17/11 Summer Graduate School (2011) Commutative Algebra (MSRI) 43 The Dirichlet Space: Connections between Operator Theory, Function Theory, and 06/20/11 to 07/01/11 Summer Graduate School (2011) Complex Analysis (MSRI) 35 IAS-PCMI Summer School on Moduli Spaces 07/03/11 to 07/23/11 Summer Graduate School (2011) of Riemann Surfaces 5 Geometric Measure Theory and Applications 07/11/11 to 07/22/11 Summer Graduate School (2011) (MSRI) 34 07/18/11 to 07/29/11 Summer Graduate School (2011) Toric Varieties in Cortona, Italy 7 Cluster Algebras and Cluster Combinatorics 08/01/11 to 08/12/11 Summer Graduate School (2011) (MSRI) 45 Seminaire de Mathematiques Superieures 2011. Metric Measure Spaces: Geometric 06/27/11 to 07/08/11 Summer Graduate School (2011) and Analytic Aspects 9

76 10/30/11 to 11/04/11 Other Scientific Workshop Chern Centennial Conference 170 Bay Area Differential Geometry Seminar 11/19/11 Other Scientific Workshop (BADGS) Fall 2011 approx. 30 Bay Area Differential Geometry Seminar 02/04/12 to 02/05/12 Other Scientific Workshop (BADGS) Spring 2012 approx. 30 Hot Topics: Thin Groups and Super-strong 02/06/12 to 02/10/12 Other Scientific Workshop Approximation 49

06/20/11 to 06/24/11 Education & Outreach Workshop Bay Area Circle for Teachers Summer 2011 approx. 40 1/28/2012 Education & Outreach Workshop Bay Area Circle for Teachers Spring 2012 approx. 40 Summer Institute for the Professional Development of Middle School Teachers 06/25/11 to 08/12/11 Education & Outreach Workshop 2011 (Wu Summer Institute) 23

08/03/11 to 08/06/11 Education & Outreach Workshop Circle onf the Road at MAA MathFest 2011 approx. 40 Critical Issues in Mathematics Education 2012: Teacher education in view of the 03/21/12 to 03/23/12 Education & Outreach Workshop Common Core 126

01/04/12 to 01/07/12 Education & Outreach Workshop Circle on the Road Joint Math Meetings 2012 approx. 40 04/13/12 to 04/15/12 Education & Outreach Workshop Circle on the Road Spring 2012 115

77 7. Appendix – Final Reports

Random Matrix Theory, Interacting Particle Systems and Integrable Systems

August 16, 2010 to December 17, 2010

Program Report

Random Matrix Theory (RMT), Interacting Particle systems (IPS) and Integrable Systems (IS)

MSRI Fall 2010

Organizing Committee

Jinho Baik (UMichigan), Alexei Borodin (MIT), Percy Deift (NYU) Alice Guionnet (ENS Lyons) Craig Tracy (UC Davis), Pierre van Moerbeke (UCL, Louvain and Brandeis University)

1. INTRODUCTION

The 2010 MSRI semester program on RMT, IPS and IS was a sequel to the highly successful program on RMT and related topics that was held at MSRI in 1999. The late 90's was a particularly exciting time in RMT: general universality results for unitary ensembles had been established and were fresh off the press, and a fundamental link had been established between Ulam's longest increasing subsequence problem in combinatorics and RMT, particularly the Tracy-Widom distribution for the largest eigenvalue of a matrix from the Gaussian Unitary Ensemble. In the 1950's Wigner had introduced RMT as a model for the scattering resonances of neutrons off a heavy nucleus, and in the 1970's Montgomery had established a remarkable link between the statistics of the zero's of the Riemann-zeta function on the critical line, on the one hand, and RMT, on the other. Now, combinatorics and related areas were in the game, and there was much anticipation of developments to come. In particular, there were key conjectures concerning both the internal structure of RMT, such as universality conjectures, as well as applications.

In the decade following 1999, the development of RMT has been explosive and many key conjectures have been settled. In particular, here are some examples, which reflect the work of many authors:

*** universality has been established for orthogonal and symplectic ensembles with very general weights, both in the bulk and at the edge

*** universality has been established for Wigner and related ensembles, both in the bulk and at the edge

*** the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, of the kind that arose in Onsager's solution of the Ising model, have been established in the general case, verifying in particular the conjecture of Basor and Tracy

*** in recent work on random particle systems/random growth models, the Asymmetric Simple Exclusion Process (ASEP) has been shown to exhibit RMT behavior. This result is particularly striking as ASEP lies outside the class of determinantal point processes. Seminal work has also been done on solutions with RMT-characteristics of the KPZ equation, which is believed to provide a universal model for wide classes of random growth processes.

*** free probability theory has emerged as a powerful tool in random matrix models, for example, in the recent proof of the "Ring Theorem" for a class of invariant non-normal matrix ensembles.

*** RMT has emerged as a key tool in multivariate statistics in the case where the number of variables and the number of samples is comparable and large. For example, there are now major applications of RMT to population genetics via Principal Component Analysis (PCA).

*** over the last year, RMT behavior has been discovered and verified in a set of laboratory experiments on turbulence in nematic liquid crystals.

*** the important role that non-intersecting Brownian motions play in RMT has been recognized and utilized in the analysis of a variety of new stochastic processes, in particular infinite-dimensional diffusions.

*** there have been major advances in understanding beta-ensembles of random matrices for general beta (alternatively, log-gases at arbitrary temperatures). In particular, the statistics of the spectra of beta-ensembles have been linked in a fundamental way to the statistics of the eigenvalues of a distinguished class of random Schrödinger operators.

*** the "Painlevé Project" has been launched. The Painlevé equations play a key role in RMT, but more generally they form the core of modern special function theory. The goal of the Project is to foster the study of the properties of the Painlevé functions, algebraic, analytical, asymptotic and numerical, and to collate the information in handbooks, as was done for the classical special functions in the 19th and 20th centuries. (See the Opinion piece in the Notices of the AMS, December 2010, for more information.)

In addition to the structural developments outlined above, there have been many direct applications of RMT. To give one striking example: the bus delivery system in Cuernavaca, Mexico, was found to obey RMT statistics. The bus system in Cuernavaca (as well as many other cities in Latin America) has certain built-in distinguishing features which are designed to avoid the bunching of buses, as well as long waits between buses.

The goal of the 2010 MSRI Program in RMT, IPS and IS was to showcase these developments as a platform for further research.

2. RESEARCH DEVELOPMENTS

Recent developments in RMT and related areas are reflected in the talks given in the three workshops and are described in greater detail in the attached Final Reports for these Workshops. The topics for the lectures in the weekly seminars (see Seminar List below) also reflect these developments. Here we will just describe some of the highlights of the Program.

*** In 2009-2010, Kazumasa Takeuchi and Masaki Sano conducted laboratory experiments on turbulence in nematic liquid crystals which demonstrated RMT-Tracy-Widom behavior in nature for the first time. This remarkable work opens up new avenues in experimental science. Takeuchi presented his work, together with more recent developments, in the December Workshop: this was one of the most memorable moments of the Program.

*** In 2009, two groups, Laszlo Erdos, Jose Ramirez, Benjamin Schlein and Horng-Tzer Yau, on the one hand, and Terry Tao and Van Vu, on the other, within a few weeks of each other, announced the proof of universality in the bulk for Wigner matrix ensembles. This solved a key 50 year old conjecture in the field. The methods of these two groups were very different and have opened up whole new avenues in the subject. A crucial element for both groups, however, was the earlier work of Erdos-Schlein-Yau on the localization/de-localization of eigenvectors of random matrices. Members of both groups spoke about their work, together with recent developments, in the first workshop.

*** In a seminal paper in 2009, Tracy and Widom showed how to solve ASEP, the asymmetric simple exclusion process, with step initial data. They found that, as in TASEP, the totally asymmetric simple exclusion process, and in the appropriate scaling limit, the behavior of ASEP was described the Tracy-Widom distribution. This result is particularly significant because ASEP, as opposed to TASEP, is not a determinantal process. Widom spoke about his work with Tracy, together with more recent developments, in the second workshop.

*** In 2010, Herbert Spohn and Tomohiro Sasamoto showed how to solve the KPZ equation explicitly for particular initial data in the appropriate scaling regime. Quite remarkably the limiting behavior is again described by RMT-Tracy-Widom behavior. The KPZ equation is the default model for the stochastic evolution of rough surfaces in 1+1 dimensions. The equation is highly singular and until the work of Spohn and Sasomoto very little was known about it's solutions. Both Spohn and Sasamoto described their work, together with recent developments, in various seminars between the workshops and also in talks during the second workshop.

*** At the same time that the paper of Spohn and Sasamoto appeared on the web, Gideon Amir, Ivan Corwin and Jeremy Quastel were writing up their work on (essentially) the same initial value problem for KPZ, obtaining the same answer in the scaling regime. In contrast to the work of Spohn and Sasamoto, the approach of Amir et al was rigorous, and utilized the earlier work of Tracy and Widom on ASEP. The work of Amir et al complements the work of Spohn and Sasamoto and is equally remarkable. Corwin spoke about their work, together with recent developments, in an Evans Lecture at Berkeley, and Quastel did the same in the second workshop.

*** The so-called tac-node process, in which two separated "clouds" of non-intersecting brownian motions come together and just touch, was analyzed over the last couple years by three different groups: Mark Adler, Patrik Ferrari and Pierre van Moerbeke; Steven Delvaux, Arno Kuijlaars and Lun Zhang; Kurt Johansson. Although all three groups obtain the same scaling limits, the formulae that they derive enroute are very different, and the differences are as yet unresolved. The interaction between Mark Adler, Kurt Johansson and Pierre van Moerbeke led to work on domino tilings of overlapping Aztec diamonds and connected the problem with the dimer models discussed by Okounkov and Reshetikhin. Members of all three groups gave talks during the weekly seminars and also during the two workshops, in which they described their work together with more recent developments.

*** Following on earlier work of Alan Edelman and Brian Sutton (2006), Jose Ramirez, Brian Rider and Balint Virag proved the striking result that the largest eigenvalue of a matrix from the beta-ensemble, the same distribution as the smallest eigenvalue of the stochastic beta-Airy operator. This seminal result established a bridge between RMT and classical stochastic analysis and provided a tool to analyze, for the first time, general beta-ensembles quantitatively. In the last year Alex Bloemendal and Balint Virag have extended this work to so-called spiked models in statistics. Bloemendal, Rider and Virag gave seminars and workshop talks about their work, together with recent developments.

*** In the Connections workshop, Alice Guionnet spoke about her proof with Mangunath Krishnapur and Ofer Zeitouni of the so-called single ring theorem for ensembles of normal matrices. The key tools in their proof are taken from free probability theory.

*** In the Connections workshop, Ioana Dumitriu and Maria Shcherbina spoke about recent developments in random matrix theory in the context of random graphs

*** In the first workshop, Nicholas Patterson spoke about his ongoing work using RMT, in the context of Principal Component Analysis, in population genetics

*** In 2009 Percy Deift, Alexander Its and Igor Krasovsky proved the conjecture of Basor and Tracy on the asymptotics of Toeplitz determinants, in the case of general Fisher-Hartwig singularities. Krasovsky spoke about their work, together with recent developments, in the first workshop.

*** In the second workshop, Doron Lubinsky spoke about his recent results proving universality for very general Unitary Ensembles.

*** N.Reshetikhin gave a well-attended semester-long weekly seminar at Evans on dimer models, with occasional seminars by the participants.

The above is only a sampling of the activity in RMT and related areas over the semester at MSRI.

3. ORGANIZATIONAL STRUCTURE

The semester was organized as follows:

*** There were three workshops. The first workshop, which took place from 13-17 September, focused on internal questions in RMT, such as universality, and also on ideas and methods from integrable systems, such as the Riemann-Hilbert Problem and the associated steepest-descent method and related ODE's and PDE's. The second workshop, the Connections for Women Workshop, took place from 20-21 September, and in addition to some of the themes in the first workshop, there were also talks on free probability and random graph theory. The third workshop took place from December 6-10, and focused mostly on the connections between RMT and random growth processes.

*** When there were no workshops, at least 2 one hour research seminars were organized each week. The speakers were chosen from scholars in residence at the time.

*** Four of the participants in the Program gave Evans Lectures at Berkeley. The Evans Lectures are sponsored jointly by MSRI and the Berkeley Math Department, and are targeted toward graduate students.

*** The postdocs - there were eight of them - organized weekly seminars amongst themselves. Each postdoc was mentored by a senior scholar in residence.

*** Many graduate students participated in the Program and the Workshop in an unofficial capacity, coming and going at various times. Five students, however, had official standing in the Program as Program Associates.

*** Two minicourses were organized, each consisting of three lectures.

The Program was extremely successful. Many senior faculty were in residence at any given time, and indeed many senior faculty stayed for the full semester; this contributed greatly to the success of the program. In addition, with few exceptions, all the leading international researchers in RMT and related areas attended the Program at one point or another. This was particularly beneficial for the postdocs and the graduate students who had the opportunity to meet and speak to the researchers who were primarily responsible for many of the developments in RMT and related areas over the last 20 years. We were proud to learn in November 2010 that Herbert Spohn, a full-time participant in the Program, had won the Heineman Prize (2011) for his work on RMT and interacting particle systems: and then in January 2011, he won the Eisenbud Prize (2011), again for his work on RMT and interacting particle systems.

4. WORKSHOPS, SEMINARS AND MINICOURSES

There were three workshops:

Random Matrix Theory and Its Applications I:

September 13-17, 2010 Organizers: Jinho Baik, Percy Deift, Alexander Its (lead organizer), Ken McLaughlin, Craig Tracy

Connections for Women: Workshop on Random Matrices

September 20-21, 2010 Organizers: Estelle Basor, Alice Guionnet (lead organizer), Irina Nenciu

Random Matrix Theory and Its Applications II:

December 6-10, 2010 Organizers: Alexei Borodin (lead organizer), Percy Deift, Alice Guionnet, Craig Tracy

The final reports are attached.

......

Here are the Authors/Titles for the seminar talks and the minicourses during the semester:

Sep 7 M.Shcherbina Universality for Orthogonal and Symplectic Ensembles Sep 8 K.McLaughlin Random matrices beyond the usual universality classes P.Bleher Exact solution of the antiferromagnetic 6-vertex model. Riemann-Hilbert approach Sep 22 T.Sasamoto Height distributions of the one-dimensional KPZ equation with sharp wedge initial conditions H.Spohn The 2-point distribution of the one-dimensional KPZ equation with sharp wedge initial data Sep 29 P.Forrester Log-gas type point processes in the complex plane C.Sinclair Two charge ensembles on the line Oct 6 A.Dembo Low temperature expansion for matrix models E.Strahov Representation theory of the infinite symmetric group and point processes of random matrix type Oct 13 L.C.Li The beta-Hermite and beta-Laguerre processes M.Duits The Gaussian free field in an interlacing particle system with two different jump rates Oct 20 M.Adler PDE's for gap probabilities and applications N.Ercolani Cycle structure of random permutations with cycle weights Oct 27 V.Gorin From random tilings to representation theory O.Zeitouni Support convergence in the single ring theorem Nov 3 M.Zworski Random matrix perturbations and quantization of tori K.Johansson Two groups of non-colliding Brownian motions Nov 10 J.Novak (MINICOURSE: First of three talks) Free probability D.Betea Elliptic distributions on stepped surfaces and an elliptic biorthogonal ensemble Nov 17 G.Benarous (MINICOURSE: First of three talks) Counting critical points of random functions in many dimensions using random matrices P.van Moerbeke The tacnode process Dec 1 A.Bloemendal Limits of spiked random matrices J.Baik Hermitian matrix model with spiked external source Dec 2 D.Romik Random sorting networks L.Bogachev Gaussian fluctuations for Plancherel partitions

5. POSTDOCTORAL FELLOWS

What follows is a description of the activities of the postdocs, in their own words.

......

Martin Bender:

PhD at Royal Institute of Technology (KTH), Stockholm, Sweden, in 2008.

Postdoc at Katholeike Univereiteit Leuven, Belgium, 2008-2010.

No current affiliation.

Mentor at MSRI: Arno Kuijlaars.

Work at MSRI: Finished previous projects resulting in the papers "Multiple Meixner-Pollaczek polynomials and the six-vertex model" (with Steven Delvaux and Arno Kuijlaars, submitted to JAP) and "Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles" (with Gernot Akemann), J. Math. Phys. 51, 103524 (2010).

Various new ideas in conjunction with the above and other problems, but nothing substantial so far.

General comments about postdoc at MSRI: The informal and friendly atmosphere was also much appreciated.

......

Vladislav Kargin:

Year of Ph.D.: 2008 Institution of Ph.D.: Courant Institute, NYU Institution and positions after Ph.D. before MSRI: Stanford University, Szego assistant professor Institution and position after MSRI: Stanford University, Szego assistant professor Mentor while at MSRI: Amir Dembo

Description of your Work while at MSRI:

While at MSRI, I studied ensembles of random matrices arising in free probability. In particular, I investigated local limit laws for the distribution of their eigenvalues. This work has been written up and submitted to a journal.

For me, the main benefit of the postdoc position at MSRI was the possibility to interact with many researchers with similar interests. It was very useful to listen to many different viewpoints. What I found especially useful was the weakly seminars. In addition, the three workshops brought together almost all researchers working in the field and were immensely interesting. In particular, the workshop "Connections for Women" was especially useful for me since many of its participants have interests that are close to mine and work on the border of free probability and random matrix theory.

The general atmosphere at MSRI was very congenial. The staff was accessible and the library and computer facilities are excellent. I would be very glad to come again.

......

Karl Liechty:

Year of Ph.D: 2010 Institution of Ph.D: Indiana University-Purdue University Indianapolis Institution and positions after Ph.D. before MSRI: None Institution and position after MSRI: Postdoctoral Assistant Professor, University of Michigan Mentor while at MSRI: Pavel Bleher

Projects worked on: Paper "Non-intersecting random walks on an interval" with P.Bleher

Monograph "Random matrix theory and the six-vertex model" with P.Bleher

In addition to these projects, on which we made substantial progress, I also discussed several potential collaborations with fellow postdocs. It remains to be seen which of these gets off the ground, but I am optimistic that something will come directly from the collaborations.

Overall, the semester was incredible for me. I probably don't even realize how much I learned over the course of the semester. There were a lot of seminars throughout the semester. The biggest difficulty for me was trying to find a balance between attending the seminars and learning new things, discussing potential collaborations, and working on existing projects.

......

Eric Nordenstam:

PhD: Swedish Royal Institute of Technology (2009) for Prof. Kurt Johansson.

Employments: July 2009 -- July 2010 Postdoc at Université Catholique de Louvain, Louvain-La-Neuve, Belgium. Working with Prof. Pierre van Moerbeke

August 2010 -- December 2010 MSRI Postdoc. Mentor: Pierre van Moerbeke

January 2011 -- December 2012 Postdoc at the University of Vienna, Austria. Working with Christian Krattenthaler.

Description:

Berkeley/MSRI is an incredibly active academic environment. There were many interesting talks and courses which took up a large amount time. Many of the leading researchers in my field were there and I learned much from them. On the whole it is very beneficial, particularly at this stage in my career, to meet famous mathematicians and be seen on the scientific stage so to speak. MSRI as a workplace is also excellent with a modern functional office building, an excellent library, money for travel and one of the world's most famous math departments just down the hill. On the whole I feel a large part of my time there was spent learning things and talking with people and less time was spent actually solving problems. I see it as an investment and I am now in a more slow paced environment in Vienna and can work through some ideas I had in Berkeley. A small sample of the collaborations and discussions I had follows.

At MSRI I met Jonathan Novak and Ben Fleming who I didn't know before. Together we came up with and studied an interesting discrete model which will certainly lead to a publication.

Ken McLaughlin, Ben Fleming and I discussed a problem of domino tilings with a certain boundary condition and also had something of a study circle on the results of Kenyon and Okounkov about limit shapes in tilings. The problem we discussed is something I certainly want to keep looking at and may yet lead to a publication.

Luen-Chau Li was also there and we discussed a model of a Laguerre distributed matrix evolving in time with a view to studying the evolution the eigenvalues of consecutive minors. It seems tractable.

I had long discussions about several problems with Peter Forrester, whom I have worked with earlier. It turned out, unfortunately, that everything we talked about was either not tractable or not interesting in the end.

In closing I would like to express my gratitude to the organizers of the program for giving me this opportunity. I should also like to thank the staff, directorate and financial benefactors of MSRI for creating this special environment and standing up for pure basic science.

......

Jonathan Novak:

Year of Ph.D.: 2009 Institution of Ph.D.: Queen's University, Canada Institution and position after Ph.D. and before MSRI: University of Waterloo, Postdoctoral Fellow Institution and position after MSRI: same as above. Mentor while at MSRI: Amir Dembo.

Description of research activity at MSRI: - Completed writing of "What is... a free cumulant?" (with P. Sniady), which will appear in Notices of the AMS, Feb. 2011 - Began work on a combinatorial approach to the Harish-Chandra-Itzykson-Zuber integral - Began work on a generalization of Schramm's characterization of the Poisson-Dirichlet distribution with parameter 1.

Description of experience at MSRI:

My experience of MSRI was certainly very positive. I had the opportunity to interact with many researchers in the field of random matrices whom I had previously known only through their publications. I learned a great deal from being able to speak with these people on a daily basis. Through the weekly seminar and the two workshops, I also gained a better sense of what the important questions in random matrix theory are, and of the direction in which the field is moving. On a professional level, it was extremely beneficial for me to be able to present my own work to seasoned researchers. I came away with a deeper understanding of how my own research programme fits into the subject as a whole, which will allow me to choose future research goals with added foresight.

......

Igor Rumanov: year of Ph.D. : 2010 Institution of Ph.D. : University of California at Davis, Davis, CA Institution and positions after Ph.D. before MSRI : none Institution and position after MSRI : University of Colorado at Boulder, Research Associate (postdoc) Mentor while at MSRI : Craig A. Tracy

While at MSRI, I learned about new directions in Random Matrix (RM) Theory related research, e.g. increasing importance of probabilistic methods, theory of stochastic differential equations (SDE), new ingenious applications of various conditioned non-intersecting Brownian Motion models to problems of statistical mechanics and combinatorics, as well as about applications of rather traditional, the well developed theory of unitary invariant RM ensembles to physics and engineering problems, e.g. wireless communication, conductance in media with impurities.

I continued to work in the directions of my previous PhD work:

1. Finished a publication:

"All the lowest order PDE's for spectral gaps of Gaussian matrices", arXiv:1008.3560

2. Worked on the derivation and properties of PDE's satisfied by the two-point distribution for the Airy process, obtained as a scaling limit of my previously derived PDE for two coupled finite size GUE matrices (in preparation).

3. Worked on possible generalization of my approach to the derivation of PDE's for spectral gap probabilities, to non-classical unitary RME (work in progress). Crucial for this work were some new things I learned from Yang Chen, and this is joint work with him.

Besides,

4. I started working on connections of the Asymmetric Simple Exclusion Process with the quantum XXZ chain.

My experience at MSRI was very pleasant. I had an opportunity to talk to many people with various areas of expertise, to get their attention, advice and, in some instances, critique of my work. The best concrete example of the benefit I derived from the program is mentioned above, under number 3. This gathering together of experts working on different problems is wonderful. I only wish that this could last longer - at least a whole year rather than just one semester. I am sure that the benefits of such an extension would grow faster than linearly with time, and thus would give more immediate, tangible results.

......

Benjamin Young: year of Ph.D.: 2008 Institution of Ph.D.: University of British Columbia Institution and positions after Ph.D. before MSRI: Centre de Recherches Mathematiques / McGill University, postdoc (2008 - 2010) Institution and position after MSRI: KTH Royal institute of technology, stockholm. Postdoc. Mentor while at MSRI: Ken Mclaughlin.

Work at MSRI: Finished and submitted two papers: arXiv:1011.0045, Title: Domino shuffling for the Del Pezzo 3 lattice Authors: Cyndie Cottrell, Benjamin Young (submitted to Transactions)

arXiv:1008.4205 Title: The Orbifold Topological Vertex Authors: Jim Bryan, Charles Cadman, Ben Young (submitted to JAMS)

4 major new projects occupied the bulk of my time at MSRI. All were centered around my usual research area (combinatorics of perfect matchings) but were, to various degrees, influenced by the random matrix theory I've been learning. All are ongoing.

1) Domino shuffling on the half hexagon lattice, joint with Eric Nordenstam. We're about to start writing the paper. 2) Asymptotics for domino tilings of an aztec diamond with a corner removed, joint with Eric Nordenstam and Ken McLaughlin. Still underway. 3) Domino shuffle for the 6-vertex model, joint with Karl Liechty. That one didn't pan out, but we now know where we went wrong, so I'm still holding out hope. 4) combinatorics of perfect matchings of "crosses-and-wrenches" graphs.

My experience at MSRI was amazing; it is an ideal place for collaboration. The biggest benefit to me was the sheer number of collaborations and the ready availability of so many experts in the field. My research plan looks much more fleshed out now than it did when I started. A secondary benefit of my postdoc at MSRI was the networking / career preparation opportunities that it afforded: I got a chance to practice my job talk; I met a lot of people from many different universities; etc. The conferences themselves were not too relevant to my work, since my research is slightly peripheral to the main thrust of work in RMT right now, but it was nonetheless very interesting to get a sense of where the field sits at the moment.

......

Anna Zemlyanova:

PhD: August 2010, Lousiana State University, Baton Rouge.

No positions before MSRI.

Starting Spring 2011: Visiting Assistant Professor, Texas A\&M University, College Station, Texas.

Mentor at MSRI: Percy Deift.

My research work is concentrated on applications of Riemann-Hilbert problems in elasticity and fluid mechanics. My main goal while at MSRI was to study direct and inverse scattering theory and the steepest descent method for Riemann-Hilbert problem in connection with NLS equation, Toda Lattice and mKdV equation. Some of the literature studied includes:

P. Deift, X. Zhou, Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space. Comm. Pure Appl. Math. 56 (2003), no. 8, 1029?1077. P. Deift, X. Zhou, A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation. Ann. of Math. (2) 137 (1993), no. 2, 295?368. S. Kamvissis, On the long time behavior of the doubly infinite Toda lattice under initial data decaying at infinity. Comm. Math. Phys. 153 (1993), no. 3, 479?519.

The proposed continuation of my work is to apply these techniques to study the long-time behavior of the Toda lattice in the collisionless shock region.

The semester at MSRI allowed me to concentrate on developing a new research area which would be difficult to accomplish otherwise. I was also able to attend research seminars and lectures at MSRI and UC Berkeley and interact with researches working in similar areas.

I gave a talk ``Application of Riemann-Hilbert Problems in Modelling of Cavitating Flow" in the postdoctoral seminar at MSRI (October 19th, 2010).

I have been able to continue working on some of my previous research problems. The result of this work is a paper ``Deformation of a supercavitating elastic curvilinear hydrofoil" written in collaboration with Yuri Antipov. Additionally, I have started working on a problem for a cascade of supercavitating flexible hydrofoils under Tulin's double-spiral-vortex model cavity closure condition. These problem reduce to Riemann-Hilbert problems in the complex plane or on an elliptic Riemann surface.

Overall, the semester at MSRI was a very positive experience and I am very thankful for the opportunity.

......

6. GRADUATE STUDENTS:

Many students attended the workshops and seminars at MSRI on an unofficial basis. Five students were officially Program Associates:

Ivan Corwin and Antonio Auffinger (students of Gerard BenArous) Dries Geudens and Adrien Hardy (students of Arno Kuijlaars) Camille Male (student of Alice Guionnet)

Corwin and Auffinger were in residence for most of the semester. The other students were in residence for just a weeks when their advisors were present.

Corwin, though still a graduate student, was chosen to give one of the Evans Lectures in the Mathematics Department at Berkeley. He is one of the rising stars in the field, and much in demand as a speaker and collaborator in this country and also abroad. As described above, he is working on RMT and interacting particle systems, and he already has an impressive publication list, as can be seen from the ArXiv. AT MSRI he seemed to be collaborating with everyone!

Auffinger is also an extremely promising researcher in RMT. At MSRI he collaborated mostly with his advisor BenArous. They are working at an intersection point of spin glasses and RMT. Their work is completely novel and provides a morse theory for a class of random functions on the sphere.

......

7. DIVERSITY:

One of our organizers was a woman (Alice Guionnet). One of our postdocs (Anna Zemlyanova) was a woman. One of our workshop participants was an African-American (Leonard Choup). The Connections for Women was very successful and well attended. Five of the speakers in the first workshop were women and three of the speakers in the second workshop were women.

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8. SYNERGISTIC ACTIVITIES:

RMT and Inverse Problems are far apart. Nevertheless, there was a reasonable amount of interaction between the programs. Participants in one program would often attend seminars in the other program. This was particularly true of the Evans Lectures and the Workshops. One of the speakers in our second workshop (Knut Solna) was from the Inverse Problems program.

......

9. NUGGETS AND BREAKTHROUGHS

Many breakthroughs and resolutions of long-standing conjectures were presented during the semester. But if one wants to single out one nugget in particular, it would have to be the experimental work of Takeuchi and Sano which demonstrated the occurrence of RMT in nature for the first time.

...... Count of Family Name Postdoc Pre/Post‐MSRI INstitution Group

Group III

Post MSRI Pre‐MSRI Foreign Group II Group I Public Group II

Foreign

00.511.522.533.54

Inverse Problems and Applications

August 16, 2010 to December 17, 2010 Report Inverse Problems and Applications, MSRI, Fall 2010

Organizing Committee: Liliana Borcea (Rice University) Maarten de Hoop (Purdue) Carlos Kenig (U. Chicago) Peter Kuchment (Texas A&M Lassi P¨aiv¨arinta (U. Helsinki) Gunther Uhlmann, chair (U. Washington and UC Irvine) Maciej Zworski (UC Berkeley)

We were fortunate to have had an exceptional number of senior researchers in residence. Of the organizers Borcea, de Hoop, Kuchment, Uhlmann and Zworski stayed for the whole semester and P¨aiv¨arinta came for two months. There were also a substantial number of leading senior researchers that participated for extended periods; this provided an excellent and rich research environment both for those researchers but more importantly for the early career participants. Eric Bonnetier, Margaret Cheney, Chris Croke, Joyce McLaughlin, Jianliang Qian, Plamen Stefanov and Andras Vasy, stayed for the duration of the program. Matti Lassas, Samuli Siltanen and Knut Solna participated for three months.

1 The Scientiﬁc Program

Inverse Problems are those where from “external” observations of a hidden, “black box” system (patient’s body, nontransparent industrial object, Earth interior, etc.) one needs to recover the unknown parameters of the system. Such problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a vast variety of of medical as well as other (geophysical, industrial, radar, sonar) imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the earth’s interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modeling in the life sciences. The field of inverse problems is broad and diverse. We briefly describe below a few of the directions of research that were emphasized during the semester, but the divisions are clearly porous. Most of the problems we outline arise from a physical situation modeled by a partial differential equation. The inverse problem is to determine some coefficients of the equation given some information about the solutions. Analysis of such problems brings together diverse areas of mathematics such as complex analysis, differential geometry, harmonic analysis, integral geometry, microlocal analysis, numerical analysis, optimization, partial differential equations, probability etc. and is a fertile area for interaction between pure and applied mathematics. Several of the participants in the semester were asked to write extended surveys on some of the topics covered during the semester for a book entitled Inside Out II. This is currently being edited and should be published in the next few months by Cambridge University Press. We list some references with work started or completed at MSRI. This list is by no means exhaustive, it intends to give a sample of some of the topics covered during the program.

Hybrid Inverse Problems Hybrid (or multi-physics, and multi-wave) imaging modalities have received a lot of attention in recent years and it was one of the central topics of research during the IP program. The MSRI-

1 Evans lecture by Lihong Wang dealt with this topic. These methods arose as an attempt to combine the high resolution of some imaging modalities and the high contrast capabilities of others. For example, in breast imaging ultrasound provides a high (sub-millimeter) resolution, while suffers from low contrast. On the other hand, many tumors absorb much more energy of electromagnetic waves (in some specific energy bands) than healthy cells. Thus using such electromagnetic waves offers very high contrast. For instance Optical Tomography (OT) is based on sending light through the body and Electrical Impedance Tomography (EIT) sends electrical currents. However OT and EIT suffer from low resolution. Examples of novel hybrid imaging methods are Photo-Acoustic Tomography (PAT), Thermoa- coustic Tomography (TAT), Ultrasound Modulation Tomography (UMT), Transient Elastography (TE) and Magnetic Resonance Elastography (MRE). PAT consists of sending relatively harmless optical radiation into tissues that causes heating (with increases of the temperature in the milli Kelvin range) which results in the generation of propagating ultrasound waves (the photo-acoustic effect). Such ultrasonic waves are readily measurable. The inverse problem then consists of reconstructing the optical properties of the tissue. In TAT, low frequency microwaves, with wavelengths on the order of 1m, are sent into the medium. The rationale for using the latter frequencies is that they are less absorbed than optical frequencies. In UMT, radiation is sent through the tissues at the same time as a modulating acoustic signal, which changes the local properties of the optical parameters (the acousto-optic effect) in a controlled manner. The objective is then the same as in PAT: to reconstruct the optical properties of the tissues. In both modalities, we seek to combine the large contrast of the optical parameters between normal and cancerous tissues with the high (sub-millimeter) resolution of ultrasound imaging. Transient Elas- tography (TE) images the propagation of shear waves using ultrasound while Magnetic Resonance Elastography (MRE) images the same shear waves using Magnetic Resonance Imaging. PAT, TAT, UMT and TE offer potential breakthroughs in the clinical application of hybrid imaging modalities to early detection of cancer, functional imaging, and molecular imaging. Hybrid methods was the subject of Peter Kuchment’s minicourse in the Introductory Workshop and several lectures during the semester and the main workshop. It is also the subject of survey papers in Inside-Out II by Guillaume Bal and Plamen Stefanov and Gunther Uhlmann. A sample of works finished or started during the program on these hybrid problems are [4], [5], [34], [35], [33], [32], [36], [37], [38], [45], [46], [47].

Inverse Boundary Problems A very important class of inverse problems are inverse boundary problems. These consist in determining the internal properties of a medium by making measurements at the boundary of the medium. These problems for instance include EIT, and OT already mentioned, seismic imaging, travel time tomography and many others. We include a brief summary of work started at MSRI during the Fall 2010 on this imaging method.

EIT and the CalderónProblem A prototypical example of an inverse boundary problem for an elliptic equation is Electrical Impedance Tomography (EIT), also called Calderónproblem. Calderónproposed the problem in the mathematical literature. In EIT one attempts to determine the electrical conductivity of a medium by making voltage and current measurements at the boundary of the medium. The information is encoded in the Dirichlet–to–Neumann (DN) map associated to the conductivity equation. One of the central issues is the case of partial data that is when measurements are made on part of the boundary. One

2 problem for which very little is known is the case that the Dirichlet data is supported in an open subset and the Neumann data is measured in a disjoint set. In [25] it was shown for a particular configuration of inputs and outputs in 2 dimensions that one can recover the conductivity. Another central issue in EIT is how the discrete problem approximates the continuous one. This is the subject of the joint work of Borcea, Guevara Vazquez and Mamonov [6]. Guevara Vazquez and Mamonov were two of the postdocs of the program. The mathematics of EIT applies also to the case of OT in the diffusion approximation where one probes the medium with light instead of electrical currents. The Calderónproblem can be formulated for more general equations than: the conductivity equation and also manifolds. For example the following works were started and or finished at MSRI. The case for systems in 2D was considered in [2], Borg-Levinson theorem for higher order operators in [31], partial data for general second order operators in 2D in [26], partial data for the biharmonic operator in dimension three or higher in [28], partial data for the magnetic Schrdinger¨ operator on a slab in [29] and full data for the polyharmonic operator in [30]. In [3] it was considered boundary value for elastic equations with small inhomogeneities. Astala, Lassas and Päivärinta and Guillarmou and Tzou have written survey papers for Inside- Out II on developments in Calderón’sproblem in the two dimensional case. Wang and Zhou have written on the problem of determining inclusions and other defects from boundary measurements. Uhlmann’s minicourse in the Introductory Workshop reviewed several developments on Calderón’s inverse problem.

Inverse Problems in Geometry An outstanding inverse problem in geophysics consists in determining the inner structure of the Earth from measurements of travel times of seismic waves. From a mathematical point of view, the inner structure of the Earth is modelled by a Riemannian metric, and the travel times by the lengths of unit speed geodesics (rays) between boundary points. This gives rise to a typical geometric inverse problem: is it possible to determine a Riemannian metric from its boundary distance function? Physically, these are the first arrival times of geodesics (rays) going through the domain. This is known in the geophysics literature as the inverse kinematic problem and in differential geometry as the boundary rigidity problem. The boundary distance function is unchanged under any isometry which is the identity at the boundary, so the question is whether one can determine the metric up to this obstruction. The answer is no since the boundary distance function takes into account only length minimizing geodesics. Any region of the manifold with a very large metric will not be seen from the boundary distance function so one needs some restriction on the metric. One such restriction is that the manifold is simple: given any two points they can be joined by a unique geodesic and the boundary is strictly convex. The conjecture proposed by Michel is that simple Riemannian manifolds with boundary can be determined uniquely up to an isometry from the boundary distance function and this has been an active area of research. The geodesic ray transform, where one integrates a function or a tensor field along geodesics of a Riemannian metric, is closely related to the boundary rigidity problem. The integration of a function along geodesics is the linearization of the boundary rigidity problem in a fixed conformal class. The standard X-ray transform, where one integrates a function along straight lines, corresponds to the case of the Euclidean metric and is the basis of medical imaging techniques such as CT and PET. The case of integration along more general geodesics arises in geophysical imaging in determining the inner structure of the Earth since the speed of elastic waves generally increases with depth, thus curving the rays back to the Earth surface. It also arises in ultrasound imaging, where the Riemannian metric models the anisotropic index of refraction. In tensor tomography problems one would like to determine a symmetric tensor field up to natural obstruction from its integrals over

3 geodesics. The case of integrating tensors of order one corresponds to the geodesic Doppler transform in which one integrates a vector field along geodesics. This transform appears in ultrasound tomography to detect tumors using blood flow measurements and also in non-invasive industrial measurements for reconstructing the velocity of a moving fluid. The integration of tensors of order two along geodesics, also known as deformation boundary rigidity, arises as the linearization of the boundary rigidity problem. The case of tensor fields of rank four describes the perturbation of travel times of compressional waves propagating in slightly anisotropic elastic media. In work started at MSRI, Paternain, Salo and Uhlmann [44] have settled completely the tensor tomography problem for simple manifolds and proved that the ray transform is injective on symmetric tensors of any order up to the natural obstruction. The proof introduces new methods and makes a connection to the attenuated ray transforms described below and also to methods in Complex Geometry such as the Kodaira Vanishing Theorem. For non-simple manifolds we consider the behavior of all the geodesics going through the domain, not just the minimizing ones. This information is encoded in the scattering relation, which maps the point and direction of entrance of a geodesic to the point and direction of exit. The scattering relation was defined by Guillemin in the context of scattering theory. The natural lens rigidity conjecture is that for non-trapping manifolds the scattering relation plus the lengths of geodesics determine the metric up to isometry. The lens rigidity and boundary rigidity problems are equivalent for simple manifolds. There are very few results about this conjecture for non-simple manifolds. Vargo proved it for real-analytic metrics satisfying a mild condition. Croke has shown that if a manifold is lens rigid, a finite quotient of it is also lens rigid. In work started at MSRI Croke [11] proved that the torus is lens rigid. This is the first example of a lens rigid manifold with trapped geodesics. Herreros, an MSRI postdoc, and Croke considered other cases when there are trapped geodesics. In particular they showed that the flat cylinder and the flat Möbius strip are determined by their lens data [12]. They also considered the case of negatively curved cylinders with convex boundary and showed that they are lens rigid. A numerical study of theoretical methods developed for boundary rigidity and lens rigidity was done in [10]. Another transform that arises in applications is the attenuated ray transform. In the case of Euclidean space with the Euclidean metric the attenuated ray transform is the basis of the medical imaging technology of SPECT and has been extensively studied. There are two natural directions in which this transform can be extended: one is to replace Euclidean space by a Riemannian manifold, and the other is to consider the case of systems where the attenuation is given for example by a unitary connection. There has been remarkable progress in the understanding of injectivity properties of these transforms. Injectivity in the Euclidean case was proved by Arbuzov, Bukhgeim and Kazantsev and an inversion formula was provided by Novikov. Recently, Salo and Uhlmann proved that the attenuated ray transform is injective for simple two dimensional manifolds. Moreover, stability estimates and a reconstruction procedure of the function from the attenuated transform were given. In the case of systems, one considers instead of a scalar function, an attenuation given by a connection A and a Higgs field Φ on the trivial bundle. The pairs (A, Φ) often appear in the so-called Yang-Mills-Higgs theories. A good example of this is the Bogomolny equation in Minkowski (2 + 1)-space which appears as a reduction of the self-dual Yang-Mills equation in (2 + 2)-space and has been object of intense study in the literature of Solitons and Integrable Systems. In recent work started at MSRI, Paternain, Salo and Uhlmann [43] proved that the attenuated ray transform is injective for unitary pairs (A, Φ) and simple surfaces. Injectivity properties of attenuated ray transforms have several applications. One of them implemented by Paternain, Salo

4 and Uhlmann for arbitrary simple surfaces is to recover a unitary connection from the scattering data given by parallel transport along geodesics. Paternain has written a survey paper on these developments for Inside-Out II.

Cloaking Another central topic of research at MSRI was invisibility, that is how to make objects invisible to different types of waves, including electromagnetic waves, acoustic waves and matter waves. Graeme Milton an Eisenbud Professor who spent two months at MSRI in Fall 2010 gave one of the MSRI- Evans lecture on this topic. One of the proposals for invisibility has been transformation optics that takes advantage of the transformation invariance of Maxwell’s equations for electromagnetic waves and Helmholtz equations for acoustic and matter waves. Advances in metamaterials have made possible to construct the appropriate materials proposed by the theory at least for certain frequencies. Science has named Metamaterials as one of the 10 breakthroughs of the decade. In work partly done at MSRI Greenleaf et al [19] have given designs, based on an overarching mathematical principle, for devices called Schrödingerhats, acting as invisible reservoirs and amplifiers for waves and particles. Schrödingerhats (SH) for any wave phenomenon modeled by either the Helmholtz or Schrödingerequation. Lassas and Zhou [39], the latter a student associate at MSRI, considered approximate cloaking in two dimensions. The material parameters used to describe perfect cloaking using transformation optics are anisotropic, and singular at the interface between the cloaked and uncloaked regions, making physical realization a challenge. These singular material parameters correspond to singular coefficient functions in the partial differential equations modeling these constructions and the presence of these singularities causes various mathematical problems and physical effects on the interface surface. In [39], the authors analyzed two dimensional cloaking for Helmholtz equation when there are sources or sinks present inside the cloaked region. In particular, they considered nonsingular approximate invisibility cloaks based on the truncation of the singular transformations. Using such truncation they analyzed the limit when the approximate cloaking approaches the ideal cloaking. They showed that, surprisingly, a non-local boundary condition appears on the inner cloak interface. In [40] a thorough study was done of approximate cloaking for Maxwell’s equations with an active source. Fernando Guevara Vazquez, Graeme Milton and Daniel Onofrei (a visitor for a month) in work done at MSRI have proposed a different method for making objects invisible [20], [21] that uses active devices to hide the object without completely surrounding it. The principle to design such invisibility devices is the same as that of noise cancelling headphones. The devices are tailored to cancel the incoming wave in some region without revealing their position from far away. Thus any object inside this region will be invisible, regardless of its shape. One disadvantage of the method is that one needs to know the incoming wave in advance.

Random Media Another topic of interest in the program and the subject of the MSRI-Evans lecture by Liliana Bocea and her minicourse in the Introductory Workshop was direct and inverse problems in random media. This was also the topic of the minicourses by Tsogka in the Connections for Women Workshop. Relatively recent work on time reversal of waves in a random medium has shown that medium fluctuations are not necessarily detrimental to, but may in fact enhance various operations with waves. In interferometry, one considers “field-field” cross correlations associated with (ambient)

5 noise observed at pairwise distinct receivers, to obtain an “empirical” Green’s function, which process is naturally related to time reversal. Indeed, results have been obtained rigorously, where the cross correlation yields the Green’s function up to an integral operator the kernel of which is described by an Ito–Liouville equation, which admits, under certain conditions, statistically stable solutions. Indeed, better estimates (when the Green’s function is better resolved) may be obtained in a randomly inhomogeneous medium than in a deterministic homogeneous medium, as a consequence of the wider angular spread in the phase-space representation of a wave in the random medium. The enhanced resolution occurs due to an exponential damping factor that appears in the analysis of the cross correlation, and that involves the structure function of the medium. The cross-correlation technique has been successfully applied perhaps most notably to the Apollo 17 Lunar Seismic Profil- ing Experiment. The correlations were used in an inverse problem estimating the thermal diffusivity in the shallow lunar crust, while heating from the Sun is the ultimate cause of the seismic noise. Effectively using receivers as sources through the mentioned “field-field” cross correlations, one can generate, in principle, a rich set of data or even a Neumann-to-Dirichlet map on part of the surface (boundary of a manifold describing the subsurface), even where deterministic sources are necessarily absent. While current studies relating to the heterogeneous earth mostly make use of surface-wave contributions to the Green’s function estimate, the importance of understanding the behavior of (scattered) body waves has been recognized. The goal of sensor array imaging is to create maps of the structure of inaccessible media using sensors that emit probing pulses and record the scattered waves, the echoes. We call the recorded echoes array data time traces, to emphasize that they are functions of time. Because the array has finite size and the data is band limited, we cannot determine in detail the medium structure, and the inverse problem must be formulated carefully to be solvable. In general, we distinguish between determining singularities in the wave speed, which arise at boundaries of reflectors, and the background speed. The latter determines the kinematics of the data, the travel times of the waves, and the former is responsible for the dynamics of the data, the reflections. Array imaging is typically concerned with locating the reflectors in the medium, but in order to be carried out it requires knowledge of the background wave speed, or its determination by other methods. Some papers on this subject started or finished at MSRI are [1], [7], [8], [9], [18].

Scattering on Manifolds A breakthrough during the semester was done by Andras Vasy [48] who developed a compelling new way of doing scattering theory for the Laplacian on Riemannian conformally compact spaces, including non-trapping high energy bounds for the analytic continuation of the resolvent in appropriate circumstances, by appropriately extending the problem to a larger space. The resulting problems are non-elliptic, but ﬁt into a very nice microlocal framework on manifolds without boundary, so the tools are very transparent. The microlocal machinery being used is also very useful in many other settings including asymptotically hyperbolic spaces and Lorentzian geometries including Kerr-de Sit- ter spaces. Vasy wrote a survey paper on this topic for the Inside-Out II developing this approach in detail for asymptotically hyperbolic spaces.

2 Workshops

There were three workshops during the program. The Connections for Women Workshop, The Introductory Workshop and the Research Workshop.

Connection for Women Workshop, August 19-20, 2010

6 Organizing Committee: Tanya Christiansen (University of Columbia, Missouri) Alison Malcolm, (MIT) Sharil Moskow (Drexel University) Chrysoula Tsogka (University of Crete) Gunther Uhlmann, chair (U. Washington and UC Irvine)

The workshop consisted of four minicourses of 2 hours each that gave an introduction to several of the topics discussed in the Introductory Workshop the following week as well as topics that will be discussed during the Fall semester. A brief description of each minicourse follows.

• An Introduction to Microlocal Analysis Lecturer: Tanya Christiansen (U. of Missouri, Columbia)

Microlocal analysis is useful in understanding solutions of differential equations. Pseudodif- ferential operators arise, for example, in inverting elliptic differential equations. The lecturer introduced pseudodifferential operators and their mapping properties. The notion of “wave front set” of a function was introduced and it was shown that is very helpful in describing its singularities.

• An Introduction To Seismic Imaging Lecturer: Alison Malcolm (MIT)

This course gave a broad overview of seismic imaging techniques, highlighting their underlying relationships to imaging in other ﬁelds (e.g. radar and ultrasound). We will begin with the Generalized Radon Transform, progress to one-way methods using a microlocal splitting of the wave equation into up- and down-going waves, and ﬁnish with a discussion of so-called reverse- time migration in which the full wave equation is run backwards in time to form an image. The approximations underlying each method and their relative importance were discussed as well as extensions beyond single-scattering.

• An Introduction to Asymptotic Expansions for Small Inhomogeneities in EIT and Related Problems Lecturer: Sharil Moskow (Drexel U.)

In this course the lecturer explained the basic tools and derivation of series expansions for potential data in the presence of small volume inhomogeneities which are diﬀerent from a smooth background conductivity. We explain what properties can be recovered from the series terms and give a few ideas about how these expansions can be used to do inversion.

Lecturer: Chrysoula Tsogka (U. of Crete) In this course the lecturer considered the problem of arrayimaging in cluttered media, in regimes with signiﬁcant multiple scatteringof the waves by the inhomogeneities. In such scat- teringregimes, the recorded traces at the array have long and noisy codasand classic imaging methods give unstable results.Statistically stable imaging methodologies for imaging in such regimes were discussed.

7 Introductory Workshop, August 23-27, 2010

Organizing Committee: Margaret Cheney (RPI) Gunther Uhlmann, chair (U. Washington and UC Irvine) Michael Vogelius (Rutgers) Maciej Zworski (UC Berkeley)

The workshop consisted of six mini-courses: • Imaging in Random Waveguides (3 lectures) Lecturer: Liliana Borcea (Rice U.)

The topic was the problem of imaging sources/scatterers in random (i.e., with large wave speed fluctuations) waveguides, using measurements of the acoustic pressure field recorded at a remote array of sensors, over some time window. The problems of imaging in random media have been addressed very actively in the recent several years, and the lectures addressed a new direction in this area, which uses the asymptotic theory of wave propagation in such waveguides developed by W. Kohler, G. Papanicolaou and J. Garnier. It was shown how this leads to a robust imaging in such waveguides. A novel incoherent imaging approach was described, based on a special form of transport equations. Recent results by the lecturer, L. Issa, and C. Tsogka were presented. The imaging in random media, albeit being more and more popular lately, is still not known sufficiently well to the inverse problems community, and thus the lectures provided an invaluable introduction to that topic. • Introduction to Radar Imaging (3 lectures) Lecturer: Margaret Cheney (RPI) Radar (and the similar sonar) imaging modality is well known to have numerous civilian and military applications. In this series of lectures, the main mathematical techniques arising in radar imaging were presented, including in particular the ones from scattering theory, PDEs, microlocal analysis, and integral geometry. A large number of practically important issues were listed that are still unresolved and demand mathematical analysis. One of them, for instance, is addressing the non-flat, 3D structure of the Earth surface when surveyed by radar equipped airplanes. Close connections to the topics and techniques addressed in other mini-courses were noticed by the lecturer and participants.

• An Introduction to Magnetic Resonance Imaging (3 lectures) Lecturer: Charles Epstein (U. Pennsylvania)

Magnetic resonance imaging is well known to be one of the major medical diagnostic and biomedical research tools. The functional MRI has already lead to many exciting discoveries. MRI is also a very common modality in chemistry studies and other areas. As in other tomographic techniques, mathematics plays a major role in MRI. The course covered the basic concepts of spin-physics needed to understand the signal equation, and sources of contrast in magnetic resonance imaging, as well as the concepts needed to understand sampling, image reconstruction, the process of selective excitation, and some of the more sophisticated applications of MRI.

8 • Hybrid Methods of Medical Imaging (4 lectures) Lecturer: Peter Kuchment (Texas A&M

Traditional tomographic methods employ the same physical kind of radiation both for pene- trating the target and for measuring the response (e.g., X-rays in the standard CT, ultrasound in ultrasound tomography, etc.). Each of these kinds of waves has its advantages and faults, e.g., one of them can provide high contrast and low resolution, while another would do just the opposite. To address these issues (as well as cost, safety, and some other parameters), a variety of new hybrid methods is being currently developed, which involve diﬀerent types of waves. The purpose is to combine the advantages of each type, while alleviating their individual deﬁciencies. These new modalities, overwied in the lectures, require new mathematical techniques . The course concentrated on the mathematical problems, results, and challenges of the hybrid modalities (thermo/photo-acoustic and acousto-electric imaging, as well as some others).

• 30 Years of Calder´on’sProblem (4 lectures) Lecturer: Gunther Uhlmann (UC Irvine and U. Washington)

In 1980 Calder´onpublished a short paper, in which he pioneered the mathematical study of the inverse problem of determining the conductivity of a medium by making voltage and current measurements at the boundary. This inverse method is also called Electrical Impedance Tomography. There has been fundamental progress made on this problem, which is now called Caldero´on’sproblem, during the following thirty years, but several fundamental questions remain unanswered. This is still an extremely active area of research. The lectures addressed the most important development – applications of complex geometrical optics. In the last lecture, counterexamples to uniqueness in Calderons problem were discussed. Studying those, the lecturer and his co-authors were led (3 years before the same result obtained by physicists) to discovery of what is now called cloaking and invisibility. The main ideas, recent results, limitations, and possible applications of the cloaking were presented.

• Electromagnetic Imaging and the Eﬀect of Small Inhomogeneities (3 lectures) Lecturer: Michael Vogelius (Rutgers U.)

A survey of work related to electromagnetic imaging was presented that spans a 20 year period. First, various representation formulas for the perturbations in the electromagnetic fields caused by volumetrically small sets of inhomogeneities were considered. The imperfections studied range from a finite number of well separated objects of known (rescaled) shape and of fixed location, to sets of inhomogeneities of quite random geometry and location. It was shown how one can use these representations to design very effective numerical reconstruction algorithms. In the second part of the lectures, the relation between small inhomogeneities and approximate invisibility was discussed. E.g., precise estimates for the degree of approximate invisibility were given. The recent approximate invisibility estimates that are also explicit (and sharp) in their dependence on frequency were also introduced.

9 All the mini-courses were enthusiastically attended by the participants and drew many questions and discussions during and between the lectures. Although the topics were diﬀerent, it was evident that close ideological and technical relations between these ﬁelds (sometimes maybe even not realized by their practitioners) exist. These links were actively discussed during and after the workshop and will most probably lead to new developments. Graduate students, postdocs, and researchers were presented a wide panorama of inverse problems topics, mathematical techniques, applications, and outstanding challenges.

Workshop, November 8-12, 2010

The well attended workshop’s goal was to assemble a large group of senior experts, junior scientists and postdocs and graduate students to assess the current state of research in various sub-fields of the theory and applications of inverse problems. In five days, 21 invited 45-min and 8 30-min lectures were presented, as well as 15 20-min contributed talks. Among those, 8 talks were delivered by postdocs and graduate students. The talks, which have attracted a large audience, have given a spectacular overview of many theoretical and applied contemporary issues of the area. Quite a few presentations were devoted to electromagnetic imaging (such as electrical impedance tomography and its mathematical incarnation - Calderónproblem), inverse scattering, and invisibility. In several lectures, close attention was paid to the development of novel imaging methods that carry a high promise for clinical diagnostics, including for instance thermo- and photo-acoustic tomography, acousto-electric tomography, multi-spectral electrical impedance imaging, bio-mechanical imaging, and new generations of ultrasound and optical imaging. Spectral inverse problems were addressed in a several talks, as well as geophysical imaging, imaging in random media, inverse problems of geometry, PDEs and relativity theory, numerical analysis issues of inverse problems. Radar theory and robust principal component analysis can also be added to this spectacular list. Although one might think that the diversity of the topics listed above is unfathomable, and the workshop should have looked like a quilt, this impression would be incorrect. In fact, everyone present at the workshop saw a seamless scientific field with numerous flourishing connections between the areas. This was also evidenced by extremely active discussions during, between, and after talks. It is clear that the communications during the workshop will lead to advances in many of the topics discussed. It is hard to predict future, especially the future research results, but one can envision for instance the methods of robust principal component analysis presented in the spectacular E. Candes’ lecture to be applied to treating motion artifacts in radar studies. The transmission eigenvalue issues, studied for a long time in the scattering theory, find new home in the novel medical imaging techniques. The geophysical techniques of plane wave stacking are being applied to improve ultrasound medical imaging. Methods developed in integral geometry of thermoacoustic imaging might be helpful in resolving some issues of radar theory, a rich field, not over-populated by mathematicians. The variety of mathematical tools involved was astounding: PDEs, integral and differential geometry, complex analysis, microlocal analysis, spectral theory, graph theory, etc. The audience contained, besides representatives of academia, also researchers from industry and research labs. These came from many countries from all over the world. It is our belief that the workshop will facilitate (and has already started doing so) new developments, collaborations, and results in the vast area of inverse problems and applications.

10 3 Postdocs

We were very fortunate to have a very active group of postdocs that collaborated among themselves or with other senior people in the program, participated in the workshops and gave talks at the MSRI workshop in November. There was also had a weekly postdoc seminar where they discussed their work. The following were the postdocs in the program.

• Kiril Datchev His mentor was Andras Vasy. Datchev worked with him in two articles on resolvent estimates [16], [17], on inverse spectral problems with Hamid Hezari (another postdoc on the program) and Ivan Ventura a student of Maciej Zworski at UC Berkeley [15]. He also wrote a related paper with Hezari on inverse problems for resonances [14]. He and Hezari have written a survey paper on inverse spectral problems for inside Out II [13]. • Fernando Guevara Vazquez His mentor was Liliana Borcea. He worked with her an Alexan- der Mamonov, another postdoc in the program, in the EIT program for discrete networks mentioned earlier [6]. Also jointly with Druskin they wrote a survey paper on this topic for Inside Out. He also wrote with Graeme Milton and other collaborators some papers on cloaking that were also mentioned earlier in the report [20], [21]. • Pilar Herreros Her mentor was Gunther Uhlmann. She studied the lens rigidity problem and wrote with Croke the paper [12] that was mentioned earlier in the report on less rigidity for two dimensional manifolds with trapped geodesics. • Hamid Hezari His mentor was Peter Kuchment. As mentioned earlier he collaborated with Kiril Datchev in several projects on inverse spectral problems and inverse problems for resonances [14], [15]. Other projects on spectral theory are [23], [24]. • Alexander Mamonov His mentor was Liliana Borcea. Mamonov worked on discrete EIT and wrote the paper [6] also mentioned above. • Linh NguyenHis mentor was Maarten de Hoop. he worked on the problem of recovering the sound speed in TAT [41]. He also studied the range characterization for a spherical mean transform on spaces of constant curvature [42]. • Juha-Matti Perki¨o His mentor was P. Stefanov. He worked on the problem of inverting the ray transform with Finsler metrics. • Leo Tzou His mentor was Gunther Uhlmann. He worked with Colin Guillarmou, a visitor for a month, on the Calder´onproblem on manifolds, including the case of the magnetic Laplacian on Riemann surfaces [22] and general two dimensional systems [2].

4 Seminars

The MSRI-Evans Lectures associated to the Inverse Problems Program were:

• Lihong Wang He discussed “Photoacoustic Tomography: Breaking through the Optical Dif- fusion Limit” on August 30, 2010.

11 • Graeme Milton September 27, 2010. He talked about “Cloaking: Where Science Meets Science Fiction” on September 27, 2010. • Margaret Cheney Her lecture was entitled “Introduction to Synthetic-Aperture Radar Imag- ing” given on September 27, 2010. • Liliana Borcea She talked on: “Detection and Imaging with Waves in Heterogeneous, Strongly Backscattering Media” on November 8, 2010.

Besides the postdoc seminar there were two seminars for week. The webpage of the seminar is: http://math.washington.edu/∼ gunther

5 Human resources

There was a strong representation by women in this program; indeed, one of the principal organizers was a woman, and women were on the organizing committees of all the workshops. Eﬀorts were made both in the planning stages and during the program to encourage participation by young mathematicians, and we had an unusually strong group of postdoctoral researchers who played in active role in the weekly seminars and the workshops. A partial list of the women participating in the program is: Liliana Borcea, Elena Beretta, Margaret Cheney, Pilar Herreros, Katya Krupchyk, Joyce McLaughling, Alison Malcolm, Anna Mazzucato, Ashley Thomas (student associate), Chrysoula Tsogka, Ting Zhou (student associate) and Miren Zubeldia (student associate).

12 References

[1] R. Alonso, L. Borcea, G. Papanicolaou, C. Tsogka, Detection and Imaging in strongly backscattering randomly layered media, Inverse Problems, 27(2011), 025004. [2] P. Albin, C. Guillarmou, L. Tzou and G. Uhlmann, Inverse boundary problems for systems in two dimensions, arXiv:1105.4565. [3] Elena Beretta, Eric Bonnetier, Elisa Francini and Anna L. Mazzucato, Small volume asymptotics for anisotropic elastic inclusions, arXiv:1105.4111. [4] Guillaume Bal, Eric Bonnetier, Fran¸coisMonard and Faouzi Triki, Inverse diffusion from knowledge of power densities, arXiv:1110.4577. [5] G. Bal, K. Ren, G. Uhlmann and T. Zhou, Quantitative thermo-acoustics and related problems, Inverse Problems, 27(2011), 055007. [6] L. Borcea, F. Guevara Vazquez and A. Mamonov, Uncertainty quantification for electrical impedance tomography with resistor networks, arXiv:1105.1183. [7] L. Borcea, J. Garnier, G. Papanicolaou and C. Tsogka, Enhanced statistical stability in coherent interferometric imaging, Inverse Problems, 27(2011), 085003. [8] L. Borcea, J. Garnier, G. Papanicolaou and C. Tsogka, Coherent Interferometric Imaging, Time Gating, and Beamforming, Inverse Problems, in press 2011. [9] L. Borcea, G. Papanicolaou and C. Tsogka, Adaptive time-frequency detection and filtering for imaging in heavy clutter, SIAM J. Imaging Science, 4(2011), 827-849. [10] E. Chung, J. Qian, G. Uhlmann and H. Zhao, An adaptive phase method with application to reflection travel time tomography, Inverse Problems, 27(2011) 115002. [11] C. Croke, Scattering rigidity with trapped geodesics, arXiv:1103.5511 [12] C. Croke and P. Herreros, Lens rigidity with trapped geodesics in two dimensions, arXiv:1103.5511. [13] K. Datchev and H. Hezari, Inverse problems in spectral geometry, arXiv:1108.5755. [14] K. Datchev and H. Hezari, Resonant uniqueness of radial semiclassical Schrodinger operators, arXiv:1107.0960 [15] K. Datchev, H. Hezari and I. Ventura, Spectral uniqueness of radial semiclassical Schrodinger operators, arXiv:1010.4835. [16] K. Datchev and A. Vasy, Propagation through trapped sets and semiclassical resolvent estimates, to appear Annales de l’Institut Fourier. [17] K. Datchev and A. Vasy, Gluing resolvent estimates via propagation of singularities, preprint. [18] M. de Hoop, J. Garnier, S. Holman and K. Solna, Scattering enabled retrieval of Green’s functions from remotely incident wave packets using cross correlations, preprint. [19] A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, Schrödinger’sHat: Electromagnetic and quantum amplifiers via transformation optics, preprint.

13 [20] F. Guevara Vasquez, G.W. Milton and D. Onofrei, Exterior cloaking with sources in two dimensional acoustics, to appear Wave Motion. [21] F. Guevara Vasquez, G.W. Milton, D. Onofrei and P. Seppecher, Transformation elastodynamics and active exterior cloaking, chapter for Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking, submitted. [22] C. Guillarmou and L. Tzou, Identification of a connection on a Riemann surface with boundary, GAFA, 21(2011), 393-418. [23] V. Guillemin and H. Hezari, A Fulling-Kuchment theorem for the 1D harmonic oscillator, arXiv:1109.0967. [24] H. Hezari and C. Sogge, A natural lower bound for the size of nodal sets, to appear Anal. and PDE, arXiv:1107.3440. [25] O. Imanuvilov, G. Uhlmann and M. Yamamoto, Inverse boundary problem with Cauchy data on disjoint sets, Inverse Problems, 27(2011), 085007. [26] O. Imanuvilov, G. Uhlmann and M. Yamamoto, Partial data for general second order elliptic operators in two dimensions, preprint. [27] J. Klein, J. McLaughlin and D. Renzi, Improving arrival time identification in transient elastography, to appear Physics of Medicine and Biology. [28] K. Krupchyk, M. Lassas and G. Uhlmann, Inverse problems with partial data for the magnetic Schrödingeroperator in an infinite slab and on a bounded domain, to appear Comm. Math. Phys. [29] K. Krupchyk and M. Lassas, Determining a first order perturbation of the biharmonic operator by partial boundary measurements, to appear Transactions AMS. [30] K. Krupchyk, M. Lassas and G. Uhlmann, Inverse boundary value problems for the polyharmonic operator, to appear Journal Functional Analysis. [31] K. Krupchyk and L. Päivärinta, A Borg-Levinson theorem for higher order elliptic operators, IMRN, 21(2011). [32] K. Krupchyk, M. Lassas and S. Siltanen, Determining electrical and heat transfer parameters using coupled boundary measurements, SIAM Journal on Mathematical Analysis, 43(2011), 2096-2115. [33] P. Kuchment and L. Kunyansky, 2D and 3D reconstructions in acousto-electric tomography Inverse Problems, 27(2011), 055013. [34] L. Kunyansky Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra, Inverse Problems, 27(2011), 025012. [35] L. Kunyansky Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries, to appear Inverse Problems in Imaging, arXiv1102.1413. [36] J. Klein, J. McLaughlin and D. Renzi, Improving arrival time identification in transient elastography, to appear Physics of Medicine and Biology.

14 [37] K. Lin, J. McLaughlin, K. Parker, K. Thomenius, D. Rubens, C. Hazard, A linear hyperbolic scheme to recover frequency dependent complex shear moduli in viscoelastic models utilizing one or more displacement data to appear, Inverse Problems. [38] K. Lin, A. Thomas, J. McLaughlin, K. Parker and D. Rubens, Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data, to appear JASA. [39] M. Lassas and T. Zhou, Two dimensional invisibility cloaking for Helmholtz equation and nonlocal boundary conditions, Math. Res. Lett., 18(2011), 473-488. [40] H. Y. Liu and T. Zhou, On approximate electromagnetic cloaking by transformation media, SIAM J. Appl. Math, 71(2011), 218-241. [41] L. Nguyen, On singularities and instability of reconstruction in thermoacoustic tomography, to appear Contemporary Mathematics. [42] L. Nguyen, Range description of a spherical mean transform on spaces of constant curvature, arXiv:1107.1746. [43] G. Paternain, M. Salo and G. Uhlmann, The attenuated ray transform for connections and Higgs ﬁelds, arXiv:1108.1118. [44] G. Paternain, M. Salo and G. Uhlmann, Tensor tomography on surfaces, arXiv:1109.0505v1. [45] J. Qian, P. Stefanov, G. Uhlmann and H. Zhao, An eﬃcient Neumann-series based algorithm for thermoacoustic and photoacoustic tomography with a variable sound speed”, SIAM Journal on Imaging Sciences, 4(2011), 850-883. [46] P. Stefanov and G. Uhlmann, Thermoacoustic tomography arising in brain imaging”, Inverse Problems, 27(2011), 045004. [47] P. Stefanov and G. Uhlmann, Recovery of a source term or a speed with one measurement and applications, to appear Transactions AMS. [48] A. Vasy, Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates, arXiv:1104.1376.

15 Count of Family Name Postdoc Pre/Post‐MSRI Institution Group

Group II

Post MSRI Group I Public Foreign Pre‐MSRI Group I Private Group I Public Group I Private Group II not ranked

Foreign

00.511.522.53

Free Boundary Problems, Theory and Applications

January 10, 2011 to May 20, 2011 Final Report Free Boundary Problems Theory and Applications

MSRI, SPRING 2011

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Final Report Free Boundary Problems Theory and Applications

September 20, 2011

Table of Contents

1. Introduction 2. Research Developments 3. Organizational Structure 4. Workshops and Conferences 5. Postdoctoral Fellows

6. Graduate Students

7. Diversity 8. Synergetic Activities

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Final Report Free Boundary Problems Theory and Applications

1. Introduction

The scientific program on Free Boundaries, Theory and Applications at MSRI, January 6-May 20, 2011, was among few programs in Free boundaries that has been supported in last few years. This very timely program was led by a group of scientists at resident at MSRI: L.C. Evans, M. Feldman, A. Petrosyan, H. Shahgholian, N. Uraltseva. Other members of organizing committee attended the program during shorter periods. The proposal of this program was initiated to gather experts in the field, from various applications of free boundary problems as well as experts in theoretical FBP. We believe that the program successfully attracted several of top ranking scientist in the field of FBP. Although the focus of the program was on the theoretical part of FBP, we were able to attract several experts in numerics and applications. This gave the program the extra advantage of more down-to-earth discussions and connections to real world problems. This aspect was highlighted in the topical workshop with several presentations in numerics and applications. As it is customary at MSRI, the program started with two successive workshops, introductory, and women connections, at early January. The introductory workshop consisted mainly of four different topics, each topic was covered during 4-lectures: 1) Toti Daskalopoulos: Degenerate Geometric Flows and related FBP-s. 2) Mikhail Feldmann: Free Boundary Problems in Shock Analysis. 3) Inwon Kim: Homogenization for free boundary problems. 4) Arshak Petrosyan: Monotonicity formulas and obstacle type problems.

2. Research Developments One of research highlights of the program was the presence of Gui-Qiang Chen who visited MSRI for a month. He collaborated with Myoungjean Bae and Mikhail Feldman on stability of Mach reﬂection conﬁguration for steady compressible Euler system. This involves studying free boundary problem with a degenerate (characteristic) condition on one of free boundaries. Also, at his talk on the workshop Free Boundary Problems, Theory and Applications , G.-Q. Chen discussed entropy waves in full compressible Euler system. This resulted in his collaboration with Steve Shkoller on existence and stability of entropy waves, which involves studying existence of short-time solutions for free boundary problems for time-dependent compressible Euler system.

The participation of Juan Luis Vazquez, a world leading expert on evolution problems and speciﬁcally porous medium equations, was fundamental and his strong and easy-going character made his guidance accessible to most of early career participants. Professor Vazquez gave a series of lectures on his topic, that attracted almost all participants as well as several others from close by places.

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Final Report Free Boundary Problems Theory and Applications

Craig Evansʼ seminars at Berkeley was a central ingredient for the program, and attracted many young participants giving them chances of presentations and interactions with other young mathematicians. H. Shahgholian and his former students, J. Andersson and E. Lindgren (both postdocs at MSRI during the program) were able to solve the long-standing open problem of optimal regularity for the obstacle-type problem with Dini-right hand side. Noemi Wolanski and Catherine Bandle worked on nonlocal diffusion problems on manifolds, existence and uniqueness of solution, spectral properties, time asymptotic and convergence to the Laplace Beltrami operator in the case of spherically symmetric manifolds (that includes as particular cases the sphere and hyperbolic space) for the conveniently rescaled operator as scaling parameter converges to zero.

3. Organizational Structure

The program structure was in principle dictated by MSRI rules, and we were advised to not overdo the activities, and keep ourselves within the suggested structure. At ﬁrst we felt that this was too much of ruling from MSRI side, but after a few weeks we realized that we needed to keep our focus.

Besides the three main workshops/conference we had weekly seminars, get togethers and other form of interactions.

We had 2h regular workshop, once a week, where each participant was given a chance to present his/her topic. In addition to this we had 2h/week lectures on a speciﬁc topic. These lectures sometimes were run with same lecturer and same topic over 2-3 weeks.

The 5-minutes postdoc seminars were also well attended and appreciated, as everyone were given a a chance to shortly present their directions of research. This was organized by one of the postdocs, E. Lindgren

Ryan Hynd also organized the series of post-doc presentations of 2*45 mins. where postdocs and other members attended, from both programs.

Juan Luis Vazquez, a leader and expert in the ﬁeld organized a brown-bag seminar. During lunch, once a week we got together and one member in 15 minu. were suppose to present a very interesting and innovative idea they or proof of a theorem. This was a great idea and created a lot of discussions.

The graduate seminar was also arranged but maybe not as successful as expected, due to not enough graduate students.

There were several other seminars regulated by MSRI: Evans talk, broken dream seminar, ...

4. Workshops and Conferences Connections for Women: Free Boundary Problems, Theory and Applications January 13, 2011 to January 14, 2011.

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Final Report Free Boundary Problems Theory and Applications

The workshop \Connections for Women: Free Boundary Problems, Theory and Applications" was a part of MSRI Program: Free Boundary Problems, Theory and Applications. The Workshop was organized by Catherine Bandle (University of Basel), Claudia Lederman (University of Buenos Aires), Noemi Wolanski (University of Buenos Aires). The Workshop was intended as a means of bringing together women working in areas related to Free Boundary Problems. Workshop included 50-min survey talks and 30-min research talks. The meeting was organized so that there was plenty of time for discussions and interactions. At the end there was a panel discussion.

Introductory Workshop: Free Boundary Problems, Theory and Applications January 18, 2011 to January 21, 2011.

To achieve our goal we opted for a mini-course format. There were four mini- courses that met for an hour a day four days in a row (Tuesday- Friday). The speakers were leaders in their ﬁeld. P. Daskalopoulos discussed free boundary problems arising in geometric analysis. M. Feldman discussed free boundary problems arising in shock analysis. I. Kim presented problems in which homogenization techniques are applied to understand free boundary problems. A. Petrosyan discussed various monotonicity formulas which play a fundamental role in understanding the regularity of the free boundary in several different problems. The talks were aimed at the postdocs in the area.

Free Boundary Problems, Theory and Applications 7/3/2011-3/11/2011.

The main purpose of the workshop was to reflect on the recent exciting developments and advancements in FBPs covering a wide spectrum of theoretical and applied topics, including: FBPs for nonlocal integro-differential operators, FBPs in hyperbolic conservation laws, Laplacian growth and Abelian sandpiles, problems governed by Navier-Stokes, p-Laplacian, porous media, and thin-film equations, quadrature domains, modeling problems in biology, elasto- plasticity, and electrowetting, homogenization of FBPs, and computational surface and interface PDEs. The breadth of the subject presents challenges and opportunities and the workshop intended to facilitate the interactions between various branches of FBPs. The speakers included distinguished members of the FBP community such as L. Caffarelli, A. Friedman, and J. Ockendon and the junior speakers such as J. Jang and L. Levine. A large number of the participants were graduate students and post-doctoral fellows, so we have encouraged speakers to include a significant introductory part in the talks and give ample motivations for the problems. In our funding too we gave priority to graduate students and the participants in earlier stages of their career with little or no access to individual or institutional grants, while encouraging more senior participants to use such grants for their expenses whenever possible. Overall, we believe that the workshop was very inspirational and stimulating for younger and more experienced FBP researchers alike, and paved the road for more exciting new developments, in the best of the tradition set in Montecantini in 1981.

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Final Report Free Boundary Problems Theory and Applications

5. Postdoctoral Fellows Eight MSRI postdoctoral fellows attended the program. Here they are in alphabetical order, together with a brief description of their research area, their mentor at MSRI and their current academic afﬁliation.

1. John Andersson, Warwick, UK (mentor: C.L. Evans), works on free boundary problem, from the regularity point of view. His interest and focus has been on problems with unstable character, and singularities of such problems.

2. Nestor Guillen, UCLA (mentor: A. Petrosyan), works mostly on problems related to the fractional laplacian. His interest are also towards problems related to Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations, and Regularity for non-local almost minimal boundaries and applications.

3. Guanghao Hong (mentor: M. Feldman), works on regularity of the Alt-Caffarelli type free boundary problem, along with symmetry properties of the solutions of the elliptic equations.

4. Ryan Hynd, Courant (mentor: H. Shahgholian), works on concavity properties of inﬁnity-laplacian ground states, and problems related to Hamilton Jacobi Equations in the Wasserstein space. His interest stretches to the analysis of eigenvalue problem of singular ergodic control.

5. Erik Lindgren, Trondheim (mentor: A. Petrosyan), Norway, works on optimal regularity aspects in free boundary problems. Specially the no-sign obstacle problem, boundary behavior and poinstwise estimates. He has some recent interest towards inﬁnity-laplace equation.

6. Henok Mawi (mentor: M. Feldman), Wroks mosty on Monge Ampere equations and related problems. AT MRI he started looking at problems in free boundaries, related to biharmonic operators.

7. Betul Orcan (mentor: H. Shahgholian), Rice, Her interest is regularity of free boundary problems, as well as homogenization of the free boundary problem in random media. Her current interest is towards the regularity and geometry of the viscosity solutions for fully nonlinear free boundary problems, and homogenization problems in Geometric Measure Theory.

8. Ko Woon Um (mentor: C.L. Evans), works on elliptic equations with singular BMO coefcients in Reifenberg domains, and also regularity for porous medium type equations with divergence-free drift. In addition to these post-docs, there were several participants at early career stage and several PhD students.

6. Graduate Students

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Final Report Free Boundary Problems Theory and Applications

The graduate students of this program came from different places. The four long term stay students came from Sweden and belonged to Shahgholianʼs group. Petrosyan had two of his students and Feldman one. Several students of C. Evans attended regularly the seminars.

Most graduate students and also postdocs were attending seminars of C. Evans at Berkeley, in parallel to other seminars at MSRI.

7. Diversity

The program attracted a large number of women mathematicians. We had more than 15 women long-term participants, along with several short term women participants. This is approximately a 1/3 of all participants.

The African-American participants were fewer than expected.

Two member of the scientiﬁc committee were Women.

8. Synergetic Activities

The two running program at MSRI, during Spring 2011, were on completely opposite poles, and scientiﬁcally it was impossible to interact unless major steps (away from each programs research area) were taken to meet any synergetic effects. However, some people might have beneﬁted from attending each others seminars, and learning one or two new things. In this regard, several problems in homogenizations are using methods from number dynamical system and are hence indirectly linked to certain aspects in Number theory, and Arithmetic statistics. This however is very fragmental in our program.

The best synergetic results were naturally the Evans Lectures, that brought us together, and specially the informal after talk meetings.

This aspect should be taken into consideration for future programs, that parallel running programs should be not so far away, topic-wise.

Henrik Shahgholian, Department of Mathematics, KTH, 100 44 Stockholm [email protected] Count of Family Name Postdoc Pre/Post‐MSRI Institution Group

Group III

Post MSRI Group II Foreign Pre‐MSRI Group I Private Group I Public Group I Public Group III

Foreign

00.511.522.53

Arithmetic Statistics

January 10, 2011 to May 20, 2011 Program report: Arithmetic Statistics, Jan-May 2011.

Organizing committee: Brian Conrey (AIM), John Cremona (Warwick), Barry Mazur (Har- vard), Michael Rubinstein (Waterloo), Peter Sarnak (Princeton), Nina Snaith (Bristol), William Stein (Washington)

1 Introduction

Number Theory has its share of conjecture and heuristics that thrive on, if not depend on, the accumulation of aggregates of instances, aggregates of numerical data. Our program stood for those aspects of number theory, be it theory or computation, that connect closely with concrete and important numerical data related to numbers themselves. To see that numerical data related to numbers themselves is also at the very heart of the pleasure of number theory, and is a major reason for the very theory itself, consider this letter of Gauss to one of his students (the italics are ours):

Even before I had begun my more detailed investigations into higher arithmetic, one of my ﬁrst projects was to turn my attention to the decreasing frequency of primes, to which end I counted the primes in several chiliads and recorded the results on the attached white pages. I soon recognized that behind all of its ﬂuctuations, this frequency is on the average inversely proportional to the logarithm, so that the number of primes below a given bound n is approximately equal to Z dn/ log(n),

where the logarithm is understood to be hyperbolic. Later on, when I became acquainted with the list in Vega?s tables (1796) going up to 400031, I extended my computation further, conﬁrming that estimate. In 1811, the appearance of Chernau?s cribrum gave me much pleasure and I have frequently (since I lack the patience for a continuous count) spent an idle quarter of an hour to count another chiliad here and there...

Often, in modern number theory, to actually sample a sufficient quantity of data that might allow you to guess even approximate qualitative behavior of the issue you are studying, you may have to go out to very high numbers. For example, there are basic questions about elliptic curves (e.g., what is the frequency of those possessing two independent rational points of infinite order) where if you only look at curves of conductor < 108, you might be tempted to make guesses that are not only wrong, but qualitatively wrong. The computational and theoretical facets of our subject form one interlocking unity. Many people in our program were engaged in the theoretical side of our subject, and many in the computational side. Much “theoretical” modern number theory bears on, and sometimes has vital need of large scale computing projects and large data-bases. And both the computational and theoretical facets connect to some of the famous heuristics in our subject: Cohen-Lenstra heuristics (average expected size of various finite abelian groups that appear in our subject); and Random matrix heuristics.

1 2 Research developments

Here are a few examples of work carried out as part of our program:

• Manjul Bhargava together with his students and co-authors have been developing extremely precise methods for counting appropriate orbits of certain arithmetic groups acting on integral points on certain lattices. This approach follows and significantly refines the classical Methods in the Geometry of Numbers (as had pursued by Gauss, Minkowski, Siegel, and others). A major application of this work of Bhargava and co-authors is to establish counts of important ingredients of the arithmetic of elliptic curves. Among their applications is the result of Bhargava-Shankar that the average rank of the Mordell-Weil group of elliptic curves over Q, when they are ordered in any of the standard ways, is < 1.5. This result is related to their study of the average size of the 2-Selmer rank of elliptic curves (again over Q , and when they are ordered in any of the standard ways). They show that the average size is three.1 For any prime number p the reduced p-Selmer rank of an elliptic curve over a number field2 has this important property: it is finite (!), computable (!) (at least in principle), and is an upper bound for the rank of the Mordell-Weil group of the elliptic curve over the number field. If the Shafarevich-Tate conjecture holds, then for all but finitely many primes p, the reduced p-Selmer rank would be equal to that Mordell-Weil rank. So it is natural, as in the results of Bhargava and co-authors alluded to above, to expect that the statistics of p-Selmer ranks (e.g., even when restricted to p = 2) contribute to our understanding of Mordell-Weil ranks. In the course of our program we learned the most recent advances in this direction (3-Selmer, 5-Selmer).

• The heuristics predicting “average sizes” of quite a few important arithmetic objects were also the focus of our program. We were fortunate to have had both Henri Cohen and Hendrik Lenstra among us. They were the co-originators of the Cohen-Lenstra heuristics that guides conjectures regarding average sizes of ideal class groups and other important invariants in number theory. The latest development in the formidable toolbox of heuristics is due to Bjorn Poonen and Eric Rains and has a somewhat different slant; it gives one precise guesses for the probabilities of reduced p-Selmer ranks for elliptic curves over a given number field (when these curves are ordered in the usual way). This too was one of the focusses of our program. A few years ago, Peter Swinnerton-Dyer, extending earlier results of Heath-Brown, studied the probabilities of reduced 2-Selmer ranks of families of elliptic curves that are quadratic twists of some very specific types of elliptic curves over Q. One grand (and enticing) feature of Swinnerton-Dyer’s study is that the probabilities arise as if they were the product of a specific Markov process; another curious feature, a drawback, perhaps, is that the statistics are dependent upon ordering the elliptic curves in the twist family not in the standard way but in terms of the number of primes dividing the discriminant. All the issues that are brought up by this work were focusses of research in our program. Specifically, Dan Kane’s work in the program was towards relating such Swinnerton-Dyer statistics dependent upon different

1Of course no 2-Selmer group can have such a size: these 2-Selmer groups are then all either above or below average. 2This is the dimension of the so-called p-Selmer group minus the rank of rational p-torsion of the elliptic curve over the number ﬁeld.

2 orderings of the collection of elliptic curves being sampled, while Karl Rubin, Zev Klagsbrun, and Barry Mazur worked on developing an approach (which has a ‘Markov Process feel’) to unconditionally prove the expected statistics for reduced 2-Selmer ranks over an arbitrary number ﬁeld for all quadratic twists families of many elliptic curves (the elliptic curves in any of these families are ordered in a certain not entirely unnatural, but again non-standard, way). In separate work, Jonathan Hanke collaborated with Bhargava and Shankar on the asymptotics for the 2-part of the class group of n-monogenic orders in cubic ﬁelds.

• Dirichlet L-functions are the simplest generalizations of the Riemann zeta-function. They were invented by Dirichlet and have been used to prove an asymptotic formula for the number of primes up to a quantity X in a given arithmetic progression modulo q. Like the Riemann zeta-function each Dirichlet L-function can be expressed as Dirichlet series (the Riemann zeta-function has Dirichlet series coefficients 1, 1, 1,... and the first Dirichlet L-function has coefficients that repeat mod 3: 1, −1, 0, 1, −1, 0,... ), has a functional equation and Euler product, and is conjectured to have its zeros on the 1/2-line; the latter assertion is sometimes called the Generalized Riemann Hypothesis. It can be proven that each individual Dirichlet L-function has at least 40% of its zeros on the 1/2-line. Conrey, Iwaniec, and Soundararajan have now shown that when all of the zeros of these Dirichlet L-functions are taken together at least 55% of these zeros are on the 1/2-line. To be specific, take a large number Q and consider all of the L-functions associated with a primitive character modulo q where q ≤ Q. Now consider all of the zeros of all of these L-functions which are located in the rectangle of complex numbers with real parts between 0 and 1 and imaginary parts between 0 and log Q. CIS proved that at least 55% of the zeros in this rectangle have real parts equal to 1/2. The technique used by CIS is something they call the ‘asymptotic large sieve.’ This is a technique which can be used to give an asymptotic formula for a quantity that would have previously been estimated by the large sieve inequality. The latter has been a staple of number theorists for more than 4 decades now. One spectacular application of the large sieve inequality is to prove the Bombieri-Vinogradov theorem which asserts that when counting primes up to X in arithmetic progressions with moduli up to Q then the error terms behave, on average, as well as could be expected, that is, as well as could be proved assuming the Generalized Riemann Hypothesis. Not surprisingly, the Bombieri-Vinogradov theorem is a much celebrated result. Indeed, Enrico Bombieri won the Fields medal in 1974 for this work. A few years ago Goldston, Pintz, and Yildirim used the BV theorem to prove their much celebrated theorem that the smallest gaps between consecutive prime numbers are an order of magnitude smaller than the average gaps. Now, with their asymptotic version of the large sieve, CIS have studied zeros on the 1/2-line, not only of Dirichlet L-functions, but of other families as well: twists of a fixed L-function of degree 2 by Dirichlet characters (at least 36% of their zeros are on the 1/2-line) and twists of degree 3 L-functions (at least one-half of one percent of their zeros are on the 1/2-line). In addition, CIS have been able to confirm a prediction from Random Matrix Theory about the sixth moment of Dirichlet L-functions at the point 1/2, averaged over characters with moduli up to Q. They prove a formula which includes all of the main terms and has an error term which is a power of Q smaller than the main terms The main terms are expressed in terms of simple factors multiplied by a ninth degree polynomial in log Q. The leading coefficient of the polynomial is 42 and the lower terms are given explicitly in terms of complicated arithemetic and geometric factors. The

3 theorem exactly matches the predictions arising from Random Matrix Theory, and provides excellent confirmation of the RMT models for L-functions. We were very fortunate to have as participants in our program, all five authors of the paper in which the predictions, now confirmed, were first detailed: Brian Conrey, David Farmer, Jon Keating, Michael Rubinstein, and Nina Snaith.

• Several of our researchers examined statistics for curves over finite fields. The zeros of the zeta function are the inverses of the eigenvalues of the Frobenius endomorphism. The work of Katz and Sarnak indicates that when the genus g is fixed and the characteristic q tends to infinity, the normalized zeros are distributed like the eigenvalues of matrices in a group of random matrices determined by the monodromy group of the moduli space of the curves. But the related question of studying statistics as q remains fixed and the genus g grows to infinity is still largely unknown, though recent progress has been made in computing the distribution of the trace of the Frobenius endomorphism for various families by Kurberg-Rudnick, Bucur- David-Feigon-Lal´ınand Bucur-Kedlaya. The broader question of computing the global distribution of the zeros in the g limit remains. This is a non-trivial modeling job, since the global obstruction imposes an infinite, but discrete, set of conditions that the matrix model should satisfy. Such a model needs to exhibit both discrete and continuous features in order to capture the global phenomenon. Bucur and Feigon, together with their collaborators, David and Lal´ınworked in this direction while at MSRI.

• Computation and experimentation played a large role in our program. For example, postdocs Jonathan Bober and Ghaith Hiary implemented Hiary’s world’s fastest algorithms for the Riemann zeta function, computing zeros of ζ(s) with =s near 1036, and using their data to test some conjectures regarding the behaviour of the zeta function. Michael Rubinstein developed general purpose algorithms for computing L-functions and also gathered extensive numerical evidence in favour of the Generalized Riemann Hypothesis. William Stein tabulated elliptic curves over Q(p(5)), and verified the Birch and Swinnerton-Dyer conjecture. John Cremona worked on his programs to systematically find curves of a given conductor over Q, with a view to doubling the range of his tables and verifying (or otherwise) that there is no curve of rank 4 and conductor less than 234446. Nathan Ryan, Nils Skoruppa, and Gonzalo Tornar´ıa,in collaboration with Martin Raum (RRST), studied methods for computing with Siegel modular forms which have degree 4 L-functions associated to them. Nils Skoruppa worked on a new algorithm for computing modular forms of half integral weight directly from the periods of the associated modular forms of integral weight. This will make it possible to tabulate half integral modular forms of very high level without the need of computing complete (and then very high dimensional) spaces as is required by the currently known algorithms. David Farmer, Stefan Lemurell, and Sally Koutsoliotas developed methods for finding Maass forms for higher rank groups and tested conjectures regarding their Fourier coefficients and associated L-functions. Jonathan Hanke worked with Gonzalo Tornar´ıa,and also collaborator Will Jagy, on classifying regular and spinor regular ternary quadratic forms, and improved the modular symbols code in SAGE to make it more suitable for computations proving finiteness theorems, and made tables of quadratic forms in 3 and 4 variables (over Q and some small number fields) together with Robert Miller.

4 √ • In the study of elliptic curves over totally real number fields like Q( 5) (recent work of William Stein) one is naturally led to Hilbert modular forms. Work of Shimura and recently of Ikeda in Japan indicates that there is a similar connection between modular forms of half integral weight and modular forms of integral weight over number fields as it is well-known for Q. However, as it is known from the theory over Q, there are several advantages to replace in such a theory the modular froms of half integral weight by Jacobi forms. The Fourier coefficients of these Jacobi forms correspond (in the theory over Q) to the central value in the critical strip of the twisted L-series of the associated Hilbert modular forms or elliptic curve over Q. Skoruppa and his student Hatice Boylan prepared a longer article to set up such a theory over arbitrary number fields based on results of Boylan’s thesis. In particular, they want, in joint work√ with Fredrik Strömberg, to compute sufficiently many examples of Jacobi forms over Q( √5) which should complement the computations of William Stein on elliptic curves over Q( 5). In the case of Siegel modular forms a conjecture of Böcherer, originally stated in the case of the forms for the full symplectic group, relates sums of Fourier coefficients of a form to the central values of its twisted spinor L-series, generalizing the formulas for the coefficients of Jacobi forms (over Q) mentioned above. Similar formulas for the case of paramodular forms were investigated by Nathan Ryan and Gonzalo Tornar´ıa.This case is of particular interest due to the so-called Paramodular Conjecture which proposes a bridge to geometry by relating spinor L-series attached to paramodular forms with Hasse-Weil L-functions attached to rational abelian surfaces (analogue to the Modularity Theorem of Wiles et al). Ryan and Tornar´ıa developed algorithms to compute Fourier coefficients of these paramodular forms in a large scale in order to carry our more extensive tests for both the Paramodular Conjecture and the paramodular extension of Böcherer Conjecture. It will also allow a large scale computation of central values of twists for degree 4 L-series, useful for testing and refining random matrix heuristics for degree 4 L-series.

3 Organizatioanl structure, workshops and conferences

Learning seminars, whereby our participants met weekly to teach each other and discuss material relevant to our research, formed an important part of our program. The Bhargava-Shankar group met to learn material related to the work of Bhargava and Shankar on ranks of elliptic curves. The explicit formula group studied the problem of ranks from an analytic perspective. The low lying zeros seminar looked at papers related to the distribution of zeros in families of L-functions. Quadratic twists of elliptic curves met to discuss the problem of ranks of elliptic curves in families of quadratic twists. Another group met during the first half of the program to study the Cohen- Lenstra heuristics and its extension to Tate-Shafarevich groups by Christophe Delaunay. Lastly, a few researchers held a seminar to study paramodular forms. The first workshop to take place as part of the Arithmetic Statistics program was the 2-day Con- nections for Women event. This targeted female mathematicians in fields related to the program, but we were pleased to see that all aspects of the workshop were well-attended by the program’s participants, which lead to a very even mix of male and female researchers. The Connections for Women workshop was a very agreeable mixture of excellent talks, a buzz of mathematical discussion and a chance to meet new people; every math workshop should be like this! The audience

5 enjoyed 6 superb talks by leading women in the area, ranging from the number theory involved in cryptography to several of the questions of counting (ranks, points on curves, number fields) that were themes of the rest of the program. The discussion session on pursuing a career in mathematics saw senior mathematicians giving advice on how to apply for first jobs and postdoctoral positions, some anecdotes about how dual- career couples have found posts in the same institution, and strategies for departments keen to increase the number of women in their faculty. With participants covering the spectrum from undergraduates to those with a long career behind them, the discussion was lively and productive. These two days then lead into the main Introductory workshop for the Arithmetic Statistics program, which most of the Connections participants stayed on to enjoy. Three other workshops formed a part of our program. Our introductory workshop was held from January 31-February 4 and featured talks to help define the direction of our program. Talks were given, in order of appearance, by: Henri Cohen, Karl Rubin, Manjul Bhargava, Michael Rubinstein, Nina Snaith, Melanie Wood, Brian Conrey, Andrew Sutherland, Jordan Ellenberg, David Farmer, John Voight, Henryk Iwaniec, Akshay Venkatesh, John Cremona, Bjorn Poonen, William Stein, Kannan Soundararajan, Chantal David, and Frank Thorne. Several of the partipants in our program were also involved in a large scale NSF funded collaborative Focused Research Group project to develop methods for computing with L-functions and associated automorphic forms, as well as verify many of the important conjectures in this area. In order to help diffuse the large mount of data being generated by the project, an archive with a user friendly front end for browsing and searching the data is being developed, and a workshop involving 15 participants was held at the MSRI, Feb 21-25, to continue developing the archive. The last workshop for our program was held April 11-15 on the theme of ‘Arithmetic Statistics’ and it highlighted some of the work carried out at the MSRI during our program. In order to give participants more opportunity to interact and collaborate fewer talks were scheduled.

4 Postdoctoral fellows

Jonathan Bober

Year of PhD: 2009 Institution of PhD: Univerity of Michigan Institution and positions after Ph.D. before MSRI: Institute for Advanced Study, member Institution and position after MSRI: University of Washington, visiting scholar Mentor at MSRI: Michael Rubinstein Publications from the program: Bounds for large gaps between zeros of L-functions, draft. The distribution of the maximum of character sums, with Leo Goldmakher, draft. New computations of the Riemann zeta function, with Ghaith Hiary, draft. Postdoc feedback: The many weekly seminars and working groups were very nice and fruitful.

Alina Bucur

6 Year of PhD: 2006 Institution of PhD: Brown Institution and positions after Ph.D. before MSRI: MIT, instructor Institution and position after MSRI: UCSD, assistant professor Mentor at MSRI: Kiran Kedlaya Publications from the program: Zeta functions of Artin-Schreier curves over finite fields, with Chantal David, Brooke Feigon, Matilde Lalin, and Kaneenika Sinha, draft. D4 curves over finite fields, with Daniel Erman, and Melanie Wood, draft.

Brooke Feigon

Year of PhD: 2006 Institution of PhD: UCLA Institution and positions after Ph.D. before MSRI: Institute for Advanced Study, postdoc. University of Toronto, postdoc. University of East Anglia, assistant professor. Institution and position after MSRI: University of East Anglia, assistant professor. City College of New York, CUNY, Assistant Mentor at MSRI: Harold Stark

Ghaith Hiary

Year of PhD: 2008. Institution of PhD: University of Minnesota. Institution and positions after Ph.D. before MSRI: University of Waterloo, IAS. Institution and position after MSRI: University of Bristol. Mentor at MSRI: D.W. Farmer. Publications from the program: Numerical study of the derivative of the Riemann zeta function at zeros, with A.M. Odlyzko, submitted. Uniform asymptotics for the full moment conjecture of the Riemann zeta function, with M.O. Rubinstein, submitted. Computing Dirichlet character sums to a powerful modulus, draft. Numerical behavior of the zeta function at large values (tentative title), with J.W. Bober, draft. Postdoc feedback: The semester included numerous informal discussion sessions and various lectures by invited visitors, both of which I found interesting and beneﬁcial. It gave me the opportunity to start interactions with several other members, including through ”FRG Fridays”. One of the highlights of the semester for me was the two excellent week-long workshops. This was a well thought-out and well organized semester.

Sonal Jain

Year of PhD: 2007 Institution of PhD: Harvard Institution and positions after Ph.D. before MSRI: Courant Institute, instructor

7 Institution and position after MSRI: Courant Institute, instructor Mentor at MSRI: Barry Mazur Postdoc feedback: The impressive group of senior faculty who were in residence through large portions of the semester were extremely beneﬁcial to me, both in building new collaborations and broadening and extending my work in new directions. I never had this sort of access to so many top people in my ﬁeld before I came to MSRI. The environment was great. Ordering lunches as a group, for example, encouraged everyone to eat together and discuss math. Afternoon tea also facilitated this.

Karl Mahlburg

Year of PhD: 2006 Institution of PhD: Univerisyt of Wisconsin, Madison Institution and positions after Ph.D. before MSRI: Princeton, visiting research fellow Institution and position after MSRI: Louisiana State University, assistant professor Mentor at MSRI: Manjul Bhargava

Robert Miller

Year of PhD: 2010 Institution of PhD: Univeristy of Washington Institution and positions after Ph.D. before MSRI: N/A Institution and position after MSRI: quid.com, senior software engineer Mentor at MSRI: John Cremona

Robert C. Rhoades

Institution of PhD: 2008. Institution and positions after Ph.D. before MSRI: Stanford University, postdoc. Institution and position after MSRI: Stanford University, postdoc. Mentor at MSRI: Audrey Terras Publications from the program: Families of Quasimodular Forms and Jaocbi Forms: The Crank Statistic For Partitions, to appear Proc. AMS. Polyharmonic Maass Forms (working title), with Jeﬀrey Lagarias, in preparation.

Kaneenika Sinha

Year of PhD: 2006 Institution of PhD: Queen’s University, Kingston, Ontario, Canada Institution and positions after Ph.D. before MSRI: Postdoctoral Fellow at University of Toronto (2006-2008), PIMS Postdoctoral Fellow at University of Alberta (2008-2010), Assistant Professor at Indian Institute of Science Education and Research Kolkata, India (2010-present)

8 Institution and position after MSRI: Assistant Professor at Indian Institute of Science Education and Research Kolkata, India

Mentor at MSRI: Henryk Iwaniec Publications from the program: The non-vanishing of central values of Rankin-Selberg L-functions, with H. Iwaniec, in preparation. Postdoc feedback: My visit to MSRI was great. I learnt a lot from my mentor, Professor H. Iwaniec and benefited from the program lectures. The library had an excellent collection of books. The peaceful atmosphere and beautiful surroundings at MSRI were highly conducive to learning and research. Gonzalo Tornaria Year of PhD: 2005 Institution of PhD: University of Texas, Austin Institution and positions after Ph.D. before MSRI: Universite de Montreal, Univer- sidad de la Republica Institution and position after MSRI: Universidad de la Republica Mentor at MSRI: Jonathan Hanke Publications from the program: A Böcherer-Type Conjecture for Paramodular Forms, with Nathan Ryan, Int J Number Theory 7 (2011), no. 5, 1395–1411. Formal Siegel Modular Forms, with Martin Raum, Nathan Ryan, Nils Skoruppa, draft. Central values of L-series for Siegel Modular and Paramodular Forms, with Nathan Ryan, work in progress. Siegel modular forms package, with Martin Rau, Nathan Ryan, Nils Skoruppa, Sage package. Fredrik Strömberg Year of PhD: 2005 Institution of PhD: Uppsala University Institution and positions after Ph.D. before MSRI: TU Clausthal, postdoc (wiss mitarbeiter). TU Darmstadt, postdoc (wiss. mitarbeiter). Institution and position after MSRI: TU Darmstadt, postdoc (wiss. mitarbeiter) Mentor at MSRI: Nils-Peter Skoruppa

Publications from the program: Newforms and spectral multiplicities for Γ0(9), submitted. Dimension formulas for vector valued Hilbert modular forms, with Nils-Peter Sko- ruppa, draft. Postdoc feedback: The program was great, it gave me the opportunity to meet and interact with many of the leading researchers in the ﬁeld.

5 Graduate students

Our program saw a large number of graduate students partipating in our program as research associates: Matthew Alderson, Sandro Bettin, Hatice Boylan, Dan Kane, Rishikesh, Gagan Sekhon, Jamie Weingadt, Shuntaro Yamagishi, Jamie Weingadt, and Kevin Wilson.

9 6 Diversity

We had a relatively large number of women participating in our program: Hatice Boyal (associate), Alina Bucur (postdoc), Alina Cojocaru (member), Chantal David (workshop organizer), Brooke Feigon (postdoc), Sally Koutsoliotas (member), Gagan Sekhon (associate), Alice Silverberg (research professor), Kaneenika Sinha (postdoc), Nina Snaith (program co-organizer and workshop organizer), Melanie Wood (member), and Audrey Terras (member).

7 Synergistic activities

Several of our participants were active in an NSF funded collaborative Focused Research Group on L-functions and modular forms. They held one week long workshop, Feb 21-25, at the MSRI during the program in order to develop their data archive and website for disseminating knowledge, software and data concerning L-functions and modular forms, and gathered as a group on Fridays in order to collaborate on the project. Four of our participants gave talks aimed at the general public at the University of California at Berkeley in the MSRI-Evans lecture series. These covered topics in number theory, the arithmetic of quadratic forms, the theory of elliptic curves, and points over ﬁnite ﬁelds. Our participants also spoke in the number theory seminar at UCB, and took part in the Arithmetic/algebraic geometry day at UCB.

8 Nuggets and breakthrough

While at the MSRI, Brian Conrey, Henryk Iwaniec, and Soundararajan completed their work on the asymptotic large sieve, which they applied to prove the exciting result that the majority of ‘zeros’ of all Dirichlet L-functions obey the Generalized Riemann Hypothesis. The Riemann hypothesis is considered by many mathematicians to be the most important unsolved problem in mathematics, and is one of the seven Clay Mathematics million dollar problems. Their proof, while not solving the Riemann Hypothesis, provides strong evidence in its favor. Manjul Bhargava, working with his graduate student Arul Shankar, discovered and proved that a positive proportion of all plane cubics fail the Hasse principle. This principle asserts the existence of rational solutions to Diophantine equations given the existence of local solutions. The fact that this priciple often fails came as a surprise to many. Two of our postdocs, Jonathan Bober and Ghaith Hiary, implemented Hiary’s world’s fastest algorithm for computing the important but poorly understood Riemann zeta function. Their record breaking computations are providing exciting new data concerning the zeta function, and yielding new insights into its true behavior.

10 Count of Family Name Postdoc Pre/Post‐MSRI Institution Group

IAS

Post MSRI Group I Public Foreign Pre‐MSRI Group I Private Group I Public Group I Private Group M not ranked

Foreign

012345 DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES

BARRY MAZUR

Very rough notes for a lecture delivered at the MSRI Workshop in Arithmetic Statistics, April 13, 2011. This represents joint work with Karl Rubin and Zev Klagsbrun.

1. The basic question The type of question we will examine has it roots in a famous result of Heath-Brown on the statistics of 2-Selmer ranks of a speciﬁc family of CM elliptic curves over Q related to the congruent number problem1. This is the family 2 3 ED : Dy = x − x for positive square-free integers D. The arithmetic of this family answers the question of whether or not D can be the common diﬀerence of an arithmetic progressions of squares of rational numbers.

This talk will present some on-going work joint with Karl Rubin and Zev Klagsbrun. The three of us are interested in rank statistics for twists of E an elliptic curve over a number ﬁeld K2. We consider arbitrary elliptic curves and arbitrary number ﬁelds. I will try to focus on the contrast between statistics in this general context and statistics over Q. Before we begin in earnest, let me give a sense of what is meant by “disparity” in the title of this lecture. By “twists” we are referring to the quadratic twist family χ {E }χ

1D.R. Heath-Brown, The size of Selmer groups for the congruent number problem, Inv. Math. 111 (1993), 171-195; see also The size of Selmer groups for the congruent number problem, II. 2We are working on this, even for twists by characters of order p where p is a general prime number despite the fact that this fascinating general question has quite a different flavor, and less immediate application, than the restricted question when p = 2. This hour I’ll talk only of p = 2. 1 2 BARRY MAZUR where χ ranges through all quadratic characters of K. Let |χ| denote the absolute value of the norm (to Q) of the conductor of χ. We shall be dealing with Selmer ranks, which—for the moment—can just be thought of as useful numbers. More specifically, It is convenient to define something that might be called the reduced Selmer rank. Definition 1.1. If E is an elliptic curve over K, by r(E; K), the reduced 2-Selmer rank of E over K, we mean: r(E; K) := {the 2 − Selmer rank of E over K} − dimF2 E(K)[2].

Among the many uses of this number r(E,K) is that it is computable, it is an upper bound for the Mordell-Weil rank of E over K, and con- jecturally it has the same parity as that Mordell-Weil rank.

Theorem 1.2. The ratio |{|χ| < X; r(Eχ; K) is odd}| |{|χ| < X}| is constant for large enough X.

Note: Here is the format of how this is proved: Let Σ be the set of all places of K dividing 2 · ∞ or the conductor of E. Let C(K) be the group of quadratic characters of K, and consider the set-theoretic mapping: C(K) −→ {even, odd} which says whether the reduced 2-Selmer rank of Eχ over K is even or odd. This mapping is constant on cosets of the kernel of the homomorphism Y h : C(K) −→ Γ := C(Kv) v∈Σ that sends χ to the product of its local restrictions χv for v ∈ Σ. More speciﬁcally, given E over K, one can deﬁne a function

fv C(Kv) −→{±1} (for v ∈ Σ) which is a slightly modified “arithmetic ratio of epsilon- factors” whose definition I omit to give here, but which has the effect that for every quadratic character χ of K, the ranks of the 2-Selmer groups of Eχ and E have the same parity if and only if Y fv(χv) = 1 ∈ {±1}. v∈Σ DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES3

Deﬁne f :Γ → {±1} to be the product: Y f(γ) := fv(γv) v∈Σ where γ = (. . . , γv,... ). Let C(K,X) ⊂ C(K) be the (ﬁnite) subgroup consisting of characters such that the absolute values of the norms of primes dividing their conductors are < X. So

C(K) = ∪X C(K,X). Since the target group Γ is finite, once X is large enough, h(C(K,X)) = h(C(K)). The limit stabilizes to the ratio |{γ ∈ Γ; f(γ) = ±1| |{|Γ| for such values of X (where the sign ±1 depends—in the evident way— on whether or not the rank of E over K is even or odd). Define, then, 1 |{|χ| < X; r(Eχ; K) is odd}| δ(E,K, odd) := − lim . 2 X→∞ |{|χ| < X}| and its colleague: 1 |{|χ| < X; r(Eχ; K) is even}| δ(E,K, odd) := − lim . 2 X→∞ |{|χ| < X}| these being called the odd and even disparities of E over K. Of course: δ(E,K, odd) + δ(E,K, even) = 0; by the disparity, 1 0 ≤ δ(E,K) := |δ(E,K, odd)| = |δ(E,K, even)| ≤ , 2 we mean the absolute value of either of the above. Whatever the disparity is—i.e., the relative frequency of odd to even ranks of the 2-Selmer groups of twists—if the Shafarevich-Tate Conjecture holds we would be getting exactly the same disparity relating odd to even ranks of the Mordell-Weil groups of twists. If δ(E,K) = 0 we “have parity” in the sense that there are statistically 1 as many odd ranks as even; and if δ(E,K) = 2 all ranks are odd, or all 4 BARRY MAZUR ranks are even. Either of these endpoints occur; for example, we show that if K has at least one real place, we “have parity.” And it is not hard to find more interesting disparities3. Here is a random example of what Zev, Karl, and I show, regarding disparity, in the course of studying full rank statistics of 2-Selmer groups.

Let L be a finite number field extension of Q of degree d, in which 2 splits completely and 5 is unramified. Form the infinite sequence of number fields Kn := L(µ2n ) for n = 3, 4, 5,... , and view the elliptic curve E (50A1) y2 = x3 − 675x − 79650 over each Kn. Theorem 1.3. 1 − 2−(2n−1+1)d δ(E,K ) = . n 2 In particular, just dealing with these examples yields a set of achieved 1 disparities that is dense in the full range of possibilities, [0, 2 ].

2. Density Again, by way of introduction, let me formulate a general conjecture regarding the relative averages of Selmer ranks of twists of a general elliptic curve E over a general number field K. Consider the function ∞ X Y 1 + 2−iZ D(Z) := D Zn = n 1 + 2−i n≥0 i=0 which has come up in the work of Heath-Brown, and later in that of Swinnerton-Dyer specifically as the stationary distribution for a certain Markov process, and has reappeared most recently as the basis of a heuristic regarding guesses for rank density averages over the range of all elliptic curves over a given number field, as formulated by Poonen and Rains. It also shows up in our work. The coefficients Dn are all positive numbers and, setting Z = 1 we get that X Dn = 1 n

3For example we show that if K has no real place, and E is semistable over K then we never “have parity.” DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES5 so D is a probability density ( a positive measure with mass equal to 1) P n on the set of natural numbers. Setting Z = −1 we get n(−1) Dn = 0 which gives us an equal balance of odd and even densities: X X 1 D = D = . n n 2 n odd n even While we are on this topic, looking ahead, if you evaluate at Z = 2 and Z = −2 you get:

∞ ∞ X Y 1 + 2−i2 Y 1 + 21−i 2nD = = = 3 n 1 + 2−i 1 + 2−i n i=0 i=0 and ∞ ∞ X Y 1 + 2−i2 Y 1 + 21−i (−2)nD = = = 0, n 1 + 2−i 1 + 2−i n i=0 i=0 respectively. This gives us that X X 3 2nD = 2nD = n n 2 n odd n even which eventually will be linked to “average sizes of 2-Selmer groups of odd and of even rank.” The derivative of D(Z) evaluated at Z = ±1 will eventually be linked to the ”average 2-Selmer (even and odd) rank.”

Here is a conjectural statement that generalizes the work of Heath- Brown to arbitrary elliptic curves and number ﬁelds.

Conjecture 2.1. (1) Let n ≥ 0, and let = “even, ” or“odd” according to the parity of n. Then the limit described the formula below exists and the formula holds:

χ 1 |{|χ| < X; r(E ,K) = n}| − δ(E,K; ) ·Dn = lim . 2 X→∞ |{|χ| < X}|

As corollaries of this conjecture (following the discussion above) one would have 6 BARRY MAZUR

Corollary 2.2. Let E be an elliptic curve over K. With the same ordering of χ’s as in the statement of Conjecture 2.1 it follows—if that conjecture holds—that the average size of the reduced 2-Selmer groups of quadratic twists of E is 3 (independent of the disparity). Moreover, there is a ﬁnite upper bound to the average 2-Selmer rank, and Mordell- Weil rank, of quadratic twists of E. The project we are currently working on is to write out a proof of a version of this general conjecture however (1) we work only under the hypothesis that the image of the Galois group of K acting on 2-torsion in E is “full,” i.e., the image is all of GL2(F2), and, more signiﬁcantly, (2) we cannot yet manage to prove these limits arranging the quadratic twists χ in order of increasing absolute value of norm of conductor as described above, but rather—at the moment—in a less satisfactory way: in terms of certain increasing boxes, to be described below.

Here are some further qualitative comments about our general methods, before becoming specific. (1) We use only standard methods: class field theory, global duality, an effective Cebotarev theorem (in either of the standard two strengths: the unconditionally proved theorem, but also if we want to improve some bounds, we formulate results using the conditional estimate based on GRH) and basic arithmetic of elliptic curves. (2) More specifically, the actual densities we obtain all derive from an understanding of the relative densities of certain “Cebotarev classes” of places in various finite extension fields of K. (3) For example, of use to us, in the context in which we work, are three distinct Cebotarev classes of “good” places of K related to the S3-extension that is the splitting field of 2-torsion in E; we call these classes types 0, 1, and 2 below according as F robv is of order 3, 2, or 1. (4) Now, averaging over many type 0 places has the effect of smoothing things out a lot, and this is a major piece of our machinery, thanks to which we avoided a certain interesting side-question4. But since I also like the feel of this—no longer necessary— question, let me record what might be the simplest example of it here: 4Zev suggested this successful way of skirting such (side-)questions. DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES7

(5) Let L/Q be, say, the cyclic (cubic) extension given by the (maximal) real subﬁeld in Q(e2πi/7). Fix a generator σ ∈ Gal(L/K) and a congruence condition m ⊂ Z (not divisible by 7) such that every ﬁnite prime P of L of degree one with norm congruent to 1 mod m has a generator π = πP ≡ 1 mod m such ∗ that π is uniquely determined modulo squares in OL by that congruence condition5. Now let p be the primes in Q ranging through the arithmetic progression for which there is a P of the above sort lying above it and form the “Legendre symbol” σ(π) π ; this is dependent only on p and not on π. Taking those primes in the arithmetic progression such that distinguishing σ(π) between primes such that π = 1, or = −1 breaks up this arithmetic progression into two classes. We’d like to know the density distribution: we think that it is 50/50. We also think that these classes are not Cebotarev classes (so there would not be a direct way of showing such a fact) but have not even been able to prove this. If anyone has any ideas about such questions, we’re interested. We thank Heath-Brown for mentioning to us that this question is similar to the question—successfully treated by John Friedlander and Henryk Iwaniec6–of how often a prime p (congruent to 1 mod 4) expressible as a2+b2 with a, b > 0 and b even has the property that the Legendre symbol a b is 1 or −1. Friedlander and Iwaniec prove that the density distribution is 50/50, but even better, they show that

X a << X1− b p

for some small, but positive . This suggests, of course, that we may be dealing here with non-Cebotarev classes of primes, since such a ﬁne upper bound for a Cebotarev class of primes is something we don’t seem to have the technology to prove at present(it would follow, though, if one could show that a sub- strip of the appropriate critical strip for the relevant L-functions were free of zeroes).

5I haven’t checked but think that m = 4 might be enough here. 6Friedlander, John; Iwaniec, Henryk (1997), “Using a parity-sensitive sieve to count prime values of a polynomial”, PNAS 94 (4): 1054-1058 8 BARRY MAZUR

3. Our initial data The essential issue has to do with quite finite data. Namely we give ourselves a (fixed) number field K with a continuous homomorphism of GK to H, the quaternionic group of order 8. We will show how this connects to elliptic curves endowed with, in effect, something *very close to* a level-4 structure7 over K.

(∗) 0 → µ2 → H → T → 0

is the exact sequence with µ2 the center of H, we will be viewing the quotient T := H/C as a vector space of dimension two over F2 with the inherited GK action,

π : GK → Aut(T ) ' GL2(F2) ' S3.

A fortiori, this representation to GL2(F2) is self-dual.

4. Quadratic spaces 1 1 We will be interested in H (K,T ) and also H (Kv,T ) for the ﬁnite, or real places v of K, noting that there is a symmetric self-pairing 1 1 2 H (K,T ) × H (K,T ) → H (K, µ2) 2 induced from cup-product and the canonical map T ⊗ T → ∧ T = µ2. Denote this pairing by angular brackets: (a, b) 7→ ha, bi, and note that it is compatible with the (corresponding) symmetric nondegenerate local pairings 1 1 2 H (Kv,T ) × H (Kv,T ) → H (Kv, µ2) = F2 for all (noncomplex) places v of K. There are a few more key ingredients here. Namely:

1 1 (1) Deﬁne Hunr(Kv,T ) ⊂ H (Kv,T ) by the exact sequence 1 1 1 0 → Hunr(Kv,T ) → H (Kv,T ) → H (L, T )

where L/Kv is the unqiue unramiﬁed quadratic extension. Call 1 1 Hunr(Kv,T ) the unramiﬁed subspace of H (Kv,T ); it is its own complement under the bilinear pairing h , iv;

7Speciﬁcally, it determines a particular form over K of the elliptic modular curve attached to the congruence subgroup Γ(4)˜ := ker{SL2(Z) → PSL2(Z/4Z)}, this being a curve of genus 0. DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES9

1 2 (2) We have the connecting map q : H (K,T ) → H (K, µ2) coming from the (nonabelian) cohomology long exact sequence derived from the exact sequence (*) above. For each v we have the 1 2 corresponding local maps qv : H (Kv,T ) → H (Kv, µ2) = F2. The relation between q and h , i is given by the formula: ha, bi = q(a + b) − q(a) − q(b); i.e., q is the quadratic function that gives rise to the symmetric bilinear form h , i. And similarly for the qv’s. (3) Such an object—a vector space with a quadratic function that gives rise to a quadratic form on it—is called a quadratic space. The product of any finite number of quadratic spaces is again a quadratic space in a natural way. In particular, for any finite Q 1 set X of places of K, the product v∈X H (Kv,T ) with quadratic function qX defined as X qX (. . . , hv,... ) = qv(hv) v∈X is again a quadratic space.

(4) We say that q is unramified at v if qv maps the unramified 1 1 subspace Hunr(Kv,T ) ⊂ H (Kv,T ) to the identity element in 1 H (Kv, µ2). Then q is unramified at all but finitely many v and (since a global cohomology class is also unramified at all but finitely many v) if c ∈ H1(K,T ), the formula X qv(c) = 0 v makes sense (since the left hand sum involves only finitely many nonzero elements) and moreover, the equation holds. 1 Definition 4.1. A subspace V ⊂ H (Kv,T ) is a Lagrangian subspace— relative to the quadratic form qv— if V is equal to its own orthogonal complement under h , iv and if qv(V ) is the identity element in µ2.

Note that almost all v have the property , then, that the unramiﬁed 1 1 subspace Hunr(Kv,T ) ⊂ H (Kv,T ) is Lagrangian. By convention (and, 1 in fact, as literally following from the deﬁnition) if H (Kv,T ) = 0 then we count 0 as a “Lagrangian subspace.”

The basic starting data is the pair (T, q) where the GK action on T cuts out an S3-extension K(T )/K. If you wish, this is a study of S3 10 BARRY MAZUR extensions of number ﬁelds, together with a small bit of extra structure 1 embodied in the quadratic map q : H (K,T ) → F2 and its localizations 1 qv : H (Kv,T ) → F2.

5. The full Selmer range for (T, q) Let Σ be a ﬁnite set of places of K containing all places dividing 2 · ∞ or ramiﬁed under the Galois action on H.

Deﬁnition 5.1. By Σ-state we mean a choice, for each v ∈ Σ of a 1 v-Lagrangian subspace in the corresponding H (Kv,T ).

Deﬁnition 5.2. A Selmer structure S on (T, q) is given by

• a choice of a ﬁnite set of places ΣS (containing all places dividing 2 · ∞ or ramiﬁed under the Galois action on H), and

• for every place v of K a choice of a v-Lagrangian subspace 1 1 HSv (Kv,T ) ⊂ H (Kv,T ) such that 1 1 – if v∈ / ΣS the v-Lagrangian subspace HSv (Kv,T ) ⊂ H (Kv,T ) is the unramiﬁed one, but – if v ∈ ΣS there is no restriction on which v-Lagrangian subspace it is. We’ll call the choice at v the v-Lagrangian (or synonymously: the local condition at v) for the Selmer structure S. There- fore the set of Selmer structures S with ΣS = Σ is in one:one correspondence with the set of Σ-states.

Deﬁnition 5.3. The Selmer subgroup 1 1 HS(K,T ) ⊂ H (K,T ) attached to a Selmer structure S on (T, q) is the subgroup consisting of those cohomology classes c ∈ H1(K,T ) that, under specialization to

GKv -cohomology, project to an element in the v-Lagrangian subgroup 1 1 HSv (Kv,T ) ⊂ H (Kv,T ) for every place v of K. DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES11

1 Theorem 5.4. The associated Selmer group, HS(K,T ), of any Selmer structure S on (T, q) is a ﬁnite dimensional F2- vector space.

One might want to understand 2-Selmer rank statistics, i.e., the behavior of the function:

1 S 7→ r(S) := dimHS(K,T )

where S ranges through S(T, q) := the set of all Selmer structures attached to (T, q). But our actual interest is, for any speciﬁc elliptic curve E over K in the moduli problem attached to (T, q), to consider the 2-Selmer rank statistics for the subset S(E) ⊂ S(T, q) consisting of Selmer structures associated to the quadratic twists, Eχ of E, where χ ranges though all quadratic characters of K (see the discussion in Sections 7, 8 and 9 below).

6. How many choices are there for local conditions of a Selmer structure at v? Suppose, for example, that v is a place of K not dividing 2 and is a place of good reduction for the elliptic curve E. The number of choices one has for v-Lagrangians depends directly on the dimension of T Gv . For unramified v, dim T Gv , in turn, simply depends on the order of the image of Frobenius at v in GL2(F2). See Table 1 below as a summary of what we are about to discuss. Say that v (not dividing 2) is of “type” 0, 1 or 2 depending upon whether dim T Gv is 0, 1 or 2. Each “type” of place forms a Cebotarev class among the allowed places of K, and under our assumption that the image of Galois is full in GL2(F2) there are infinitely many places of each type. (That there are infinitely many “type 0” places is crucial for our methods.)

1 • For the places of “type 0” the local cohomology group H (Kv,T ) vanishes and therefore qualiﬁes as its own Lagrangian subspace; hence the quotation-marks around the “1” in Table 1.

• For the places of type 1 there are only two Lagrangian, the unramiﬁed Lagrangian, and one other; hence the 1 + 1 listed in the table. 12 BARRY MAZUR

• For places of type 2 (even though we are dealing with sets of very few elements) the structure deserves some discussion: In 1 this case the dimension of H (Kv,T ) is 4. So the projectiviza- 3 tion of this four-dimensional F2- vector space is P (over F2) in which the nondegenerate quadratic form qv cuts out a smooth quadric surface V . Now, any such quadric surface is bi-ruled– i.e., there are two families (a priori, possibly conjugate over F2) of lines in V . Each line defined over F2 in the quadric V comprises a Lagrangian subspace. But, by hypothesis, the unramified maximal isotropic subspace is Lagrangian which im- plies that each of the families is defined over F2; consequently, there are six Lagrangian subspaces in all, three for each family. The unramified local condition consists of the unique unramified Lagrangian. Twisting, however, by a quadratic character only moves the local condition within the ruling containing the unramified Lagrangian as one of its members; more specifically, then, a v-ramified twist will move the local condition to one of the two “ramified Lagrangians” within the ruling containing the unramified Lagrangian.

To sum up: • for primes v (of the above sort) of type 0—which we shall also be calling the set of negligible places—we have only one choice of local condition at v;

• for primes of type 1 once we stipulate whether the Lagrangian we wish to choose is unramiﬁed or ramiﬁed, the local condition is determined;

• for primes of type 2 there are two possible choices of ramiﬁed local conditions.

7. The Selmer structure attached to an elliptic curve

Let E be an elliptic curve over K; let HE be the associated Heisen- 8 berg group with GK -action,; let

T := HE/Center = E[2]; and let q be the quadratic function associated to the GK -“module” HE. Fix a ﬁnite set Σ of places containing all places of bad reduction for E, together with all places dividing 2 · ∞ or ramiﬁed under the Galois action on H.

8This should be given in an appendix ... actually: a pretty long appendix. DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES13

The Selmer structure SE,Σ ∈ S(T, q) attached to E and Σ is given by the following prescription for its local conditions:

(1) We put ΣS = Σ, and 1 (2) for all v we choose our Lagrangian subspace HSv (Kv,T ) to be 1 1 1 HSv (Kv,E[2]) = E(Kv)/2E(Kv) ⊂ H (Kv,E[2]) = H (Kv,T ), where the inclusion in the middle comes from the standard Kummer sequence.

8. Twisting We now want to discuss twisting our Selmer structures by global quadratic characters χ of K—that is, given a Selmer structure S and a quadratic character χ, we will be interested in producing a new Selmer structure S(χ) that mimics the change in Selmer structures when we pass from that of some elliptic curve E to its twist Eχ. The story here is diﬀerent for each of the four classes of places: the ﬁnite collection in ΣS, and the places outside ΣS of each ‘type” as discussed in the previous paragraph.

(1) For v∈ / ΣS of type 0, there’s absolutely nothing that can change:–the local condition, H1 (K ,T ), as well as the full S(χ)v v 1 H (Kv,T ) is 0. It turns out to be quite an advantage for us that there is a set of places (of positive density among all places of K) of this sort: among other things we will be “averaging” over twists by characters that are ramiﬁed at those places,—noting that we haven’t changed things there— to give us control of averages over the more diﬃcult places.

(2) For v∈ / ΣS of type 1, there are only two possible v-Lagrangians, the unramified Lagrangian, and a unique ramified one. Since v 1 is not in ΣS, HSv (Kv,T ) is the unramified v-Lagrangian. The recipe giving H1 (K ,T ) is as follows: if the character χ is S(χ)v v unramified at v, then H1 (K ,T ) = H1 (K ,T ) is the unram- S(χ)v v Sv v ified v-Lagrangian, and if χ is ramified at v, then H1 (K ,T ) S(χ)v v is the unique ramified v-Lagrangian.

(3) For v∈ / ΣS of type 2 and if χ is unramiﬁed at v, then, again, H1 (K ,T ) = H1 (K ,T ) is the unramiﬁed v-Lagrangian. S(χ)v v Sv v

(4) For v∈ / ΣS of type 2 and χ ramiﬁed at v then it will also be the case that H1 (K ,T ) is ramiﬁed. Since there are only two S(χ)v v 14 BARRY MAZUR

ramiﬁed v-Lagrangians, to complete the recipe here we need only say which it is ...

(5) The ﬁnal case, for the ﬁnitely many places v ∈ ΣS it is even a trickier business to say explicitly what H1 (K ,T ) is, but, S(χ)v v again, given what we are averaging over, we need know nothing more than what we have discussed to obtain the statistics we’re looking for.

9. “Arranging” the elliptic curves that are quadratic twists of a given elliptic curve

Recall that to do statistics on these mathematical objects we have to stipulate two things: • the collection of objects to be counted, and • the way in which they are ordered.

The collection, for example, of elliptic curves given by families of quadratic twists of a given elliptic curve has some fascinating features, and deserves to be studied separately. Fixing a, b ∈ OK and varying c ∈ OK − {0} consider the family cy2 = x3 + ax + b, or—tucking the c into the left-hand side of the equation, on gets the same elliptic curve from y2 = x3 + ac2x + bc3. The elliptic curves in this family are all isomorphic over C; they are quadratic twists of one another (in various senses, but most directly:) in the sense that any two of them become isomorphic over some quadratic extension of the base field K. Note also that modifying c by multiplying by a square in OK does change the isomorphism type of the elliptic curve so what is really at issue is a class of elliptic curves indexed by elements in OK − {0} mod squares. Let us define a quadratic twist family of elliptic curves over K to be given by an elliptic curve E over K together with all its twists χ 7→ Eχ indexed by quadratic Dirichlet characters χ over K. Here we have various possible useful naturally arising choices of ordering this same collection of objects, and although sometimes one (e.g., Dan Kane) can prove a kind of robustness; i.e., that the averages DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES15 that are computed via various different orderings are the same,9 things are a bit delicate. Fix an elliptic curve E over a number field K, and Σ a finite subset of the set of places PK of K (in practice it will be required to contain the archimedean places, and the places dividing p or the conductor of E). By the natural ordering Let us mean that we arrange the members Eχ of our family by increasing absolute value of the norm (down to Q) of the conductor of χ. There are a number of equivalent way of describing this, e.g., in terms of increasing absolute value of the norm of the discriminant, or the conductor, of Eχ.

In contrast, however, to the natural ordering, our results require a slightly diﬀerent type of ordering, and we give some hints about this in the next, and last section.

10. Skew-box ordering By a skew-box ordering of our family we mean the following.

(1) First, for integers 1, 2, 3, . . . ν, . . . we give positive-real-valued monotonically increasing functions αν(X) of a positive real variable X; we assume further that for each ν αν(X) tends to in- ﬁnity with X.

(2) If χ ∈ C(K) let d(χ) be its conductor, and write it as follows:

d(χ) = dΣ(χ)d0(χ)d1(χ)d2(χ), where we have factored d(χ) into the part involving places in Σ and the places (outside Σ) of types 0, 1 and 2.

Definition 10.1. For positive integers j, k define the skew- box Bj,k(K,X) with sides {αν}ν and cuttoff X to be the finite subset of the group C(K) of quadratic characters where

0 0 (a) d1(χ) = q1q2 . . . qj0 is a product of j places, where j ≤ j and the absolute value of the norm of qi is < αi(X), for i = 1, 2, . . . j0, and where

9Of course, naturally arising is a key phrase here: one can perversely order inﬁnite collections of objects to mess up things. 16 BARRY MAZUR

0 (b) d2(χ) = qj0+1qj0+2 . . . qj0+k0 is a product of k places, where 0 k ≤ k and the absolute value of the norm of qi is < αi(X), for i = j0 + 1, j0 + 2, . . . j0 + k0,

(c) (in contrast to the requirement that we bound the norms of each of the places of types 1 and 2, and take account of how many places of those types there are) we require that the absolute value of the norm of d0(χ) is < αj0+k0+1(X).

Note that C(K) is the union of the ﬁnite “skew-boxes” Bj,k(K,X) as X, j, and k tend to inﬁnity.

Here is our theorem:

Theorem 10.2. Let E be an elliptic curve over K with full Galois action on 2-torsion; that is, the natural homomorphism Gal(K/K¯ ) −→ AutE(K¯ )[2] is surjective. For integers 1, 2, 3, . . . ν, . . . there are explicit positive-real-valued monotonically increasing func- 10 tions αν(X) of a positive real variable X, each tending to inﬁnity with X, such that deﬁning skew-boxes Bj,k(K,X) with sides given by those {αν}ν, we have: (1) Let n ≥ 0, and let = “even, ” or“odd” according to the parity of n. Then the limit described the formula below exists and the formula holds:

10These functions depend on E and K. I won’t give the formulas here, but just mention that these are deﬁned “recursively” and come from successively applying the eﬀective Cebotarev Theorem; we have unconditional bounds, and also better bounds conditional on GRH. DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES17

χ 1 |{χ ∈ Bj,k(K,X); r(E ,K) = n}| −δ(E,K; ) ·Dn = lim lim 2 j+k→∞ X→∞ |Bj,k(K,X)| where X, j, and k all go to inﬁnity.

As discussed in the context of Conjecture 2.1 a series of corollaries follow: Corollary 10.3. Let E be an elliptic curve over K with full Galois action on 2-torsion. With the same skew-box ordering of χ’s as in the statement of Theorem 10.2 the average size of the reduced 2-Selmer groups of quadratic twists of E is 3 (independent of the disparity). Moreover, there is a ﬁnite upper bound to the average 2-Selmer rank, and Mordell-Weil rank, of quadratic twists of E. 18 BARRY MAZUR Table 1. Basic Count

Gv 1 1 Type order of F robv in Aut(T ) dim T dim H (Kv,T ) # of Lagrangians in H (Kv,T ) 0 3 0 0 “1” 1 2 1 2 1+1 2 1 2 4 1+2

Complementary Program

August 16, 2010 to May 20, 2011

Report from Postdoctoral Fellow Jacob White:

Fall 2010

I submitted three papers for publication - one with coauthors Helene Barcelo and Christopher Severs, another with Christopher Severs, and one as the only author. The last one, on a problem involving polynomial invariants of hypergraphs, was accepted in Electronic Journal of Combinatorics. I also regularly attended a reading group in Topological Combinatorics that was organized by Alexander Engstrom, of UC Berkeley, and Anton Dochtermann, of Stanford University. I also collaborated with Volkmar Welker during his brief visit, which led to some new ideas which require further exploration. Finally, I met with Marcelo Aguiar during a talk at UC Berkeley, which has led to ongoing collaboration through email involving combinatorial species and Hopf algebras.

Spring 2011

I collaborated Fatemeh Mohammadi, who was also in the complementary program. We worked on a few problems and ideas in combinatorial commutative algebra. While the experience did not lead to a publication, it did increase my knowledge of the subject immensely, particularly since some of the proof techniques are related to my thesis work. I also studied problems related to complexity theory, signed graphs, and topological combinatorics. This work is currently in the process of being written up for publication.

Possible Improvements

There is one problem that might need to be addressed in the future. One issue with being in the Complementary program is that the mentoring process is not as thorough as the mentoring process for the special programs. In order to maximize our development, Fatemeh and I needed to collaborate with people outside of the institute. However, nonmembers tended to be too busy to work with. People in the special programs tended not to have this challenge, as their mentors were members, and hence were usually focused on all aspects of the special programs, including the mentoring process. I am not sure how this might be improved, aside from always making sure that postdocs in the complementary program have a natural choice of mentor from someone else in the complementary program.

Count of Family Name Postdoc Pre/Post‐MSRI Institution Group

Pre‐MSRI Post MSRI Group II Group II

0 0.2 0.4 0.6 0.8 1

Random Matrix Theory and Its Applications I September 13 to 19, 2010 MSRI, Berkeley, CA, USA

Organizers: Jinho Baik (University of Michigan) Percy Deift (Courant Institute of Mathematical Sciences) Alexander Its* (Indiana University-Purdue University Indianapolis) Kenneth McLaughlin (University of Arizona) Craig A. Tracy (University of California, Davis)

Parent Program: Statistical Challenges for Meta-Analysis of Medical and Health-Policy Data Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

November 10, 2010

Report on the MSRI workshop “Random Matrix Theory and Its Applications I” September 13 - 17, 2010

Organizers.

• Jinho Baik (University of Michigan) • Percy Deift (Courant Institute) • Alexander Its (Indiana University -Purdue University Indianapolis) • Kenneth McLaughlin (University of Arizona) • Craig Tracy (University of California, Davis)

1. Scientiﬁc description

Random matrix theory (RMT) was introduced into the theoretical physics community by Eugene Wigner in the 1950s as a model for scattering resonances of neutrons off large nuclei. In multivariate statistics, random matrix models were introduced in the late 1920s by John Wishart and subsequently developed by Anderson, James and others. Since these early beginnings RMT has found an extraordinary variety of mathematical, physical and engineering applications. Indeed, the distributions of random matrix theory govern statistical properties of a rapidly increasing number of large systems which do not obey the usual laws of classical probability, and which range from heavy nuclei to polymer growth, high-dimensional data analysis, statistical mechanics and to number theory. Random matrices also represent one of the crossroads of modern mathematics. The study of random matrix theory is an extraordinary fusion of ideas and techniques from many different fields that include functional analysis, representation theory, stochastic analysis, Riemann-Hilbert problems, topology, and integrable systems, amongst many others. In the spring of 1999, MSRI hosted a very successful and influential one- semester program on RMT and its applications. The goal of the 2010 Program is to showcase the many remarkable developments that have taken place since 1999 and to spur further developments in RMT and related areas of interacting particle systems and integrable systems as well as to highlight various applications of RMT. This workshop was the first workshop of the new program, and it focused on the following aspects of the current research activity in RMT. 1. Universality in RMT. 2. RMT and statistics 3. Partition functions and RMT 4. Riemann-Hilbert and operator methods

Page 2 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

In addition, the workshop featured topics related to multi-matrix and normal models, random processes, combinatorics of alternate matrices, and also some of the most recent applications of RMT which have emerged in biology and in wireless communication technology. The workshop has also clearly demonstrated that the directions of the development of the field that were formulated and had their origins at the time of the first MSRI random matrix program proved to be well choosen. Indeed, several challenging problems that were open ten years ago have now been solved and, in turn, have yielded new areas of research and new problems. Also, a new generation of the leaders in the field has matured. In fact, many of the key speakers of this workshop were junior participants in the first program. From this perspective, it is very significant that in this workshop there was again a very strong contingent of young researchers who will certainly soon become well known to the mathematical community at large. In this respect it is worth mentioning that one of the Evans lectures, which are traditionally organized in conjunction with a program, was given this semester by Ivan Corwin who is still a fourth year PhD student.

2. The workshop’s highlights

Regarding universality questions, the workshop featured one of the most remarkable recent results in RMT - the proof of the sine-kernel universality for Wigner matrices. This result dramatically extends the class of random matrix ensembles sharing the same universal local eigenvalue statistics as the invariant ensembles, and it was obtained in the series of works of Erdös,Péché,Ram´ırez, Schlein, and Yau, and also in the works of Tao and Vu. The lectures on this subject were given by H.-T. Yau and by T. Tao, respectively . There were also two talks - the talks of T. Grava and T. Claeys, where the RMT was shown to surface in the critical behavior of solutions of nonlinear PDEs. The universality issue was also a major topic in the Evans lecture given by Ivan Corwin. This lecture surveyed the appearance of RM universalities in the theory of random processes. In particular, it was demonstrated that the Tracy-Widom distributions are an intrinsic component of the KPZ-universality class. Another big topic of the workshop was the partition functions of random matrix theory and related statistical mechanics models. The first talk on this topic was given by Philippe Di Francesco, and it was concerned with the evaluation of the generating function for planar maps with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. Di Francesco showed in his talk that the relevant scaling limit yields the stationary KdV hierarchy - the so-called Novikov equations, in place of the continuous string equations of the standard matrix model. The intrinsic meaning of this intriguing phenomenon is still open as well as the question of whether there exists a matrix integral representation for the generating function studied by Di. Francecso and his collaborators. The theme of topological enumeration was continued in Nick Ercolani’s and Alice Guionnet’s lectures. In his talk, Ercolani revisited the classical Bessis- Itzykson-Zuber genus expansion of the hermitian matrix integral and derived explicit formulae for the coefficients of this expansions as functions of the cou- pling parameter proving, in particular, the old BIZ conjecture. The lecture of Guinonet was devoted to the representations of certain loop models as matrix

Page 3 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

models, in fact, as multi-matrix models. She reported some very recent results concerning the evaluation of the planar limits of these matrix models and explained their combinatorial meaning. Two talks were devoted to yet another hot issue of the field - to general beta-ensembles. In Brian Rider’s talk, a stochastic definition of the Tracy- Widom distribution TWβ for general β was given. This result is a breakthrough in the old issue of describing the limiting edge distribution in general beta- ensembles. Several extremely challenging questions remain. Among them are: (a) the analog of Painlevé-type representation for TWβ for general β > 0 and (b) the complete tail asymptotics for TWβ for general β. Regarding the last question, very interesting results were presented in the second general beta talk by GaëtanBorot. Borot described a heuristic approach, which he has developed with Eynard and others, to the derivation of the left tail asymptotics of TWβ. The approach of Borot et al. is based on an a priory assumption on the structure of the large N expansion of the β - integral. The two talks on Toeplitz determinants - given by E. Basor and I. Krasovsky - presented the state of art in this classical area which has experienced renewed development in the last decade. Basor reported on her very recent results with Ehrhardt on a wide class of perturbed Toeplitz determinants which includes the Toeplitz+Hankel determinants which are particularly important for random matrix applications. The lecture of Krasovsky focused on the Riemann-Hilbert approach to Toeplitz determinants. In particular, Krasovsky described the use of this approach in the recent proof (Deift, Its, Krasovsky) of the long-standing conjecture of Basor and Tracy concerning the asymptotics of the Toeplitz determinants with general Fisher-Hartwig type symbols. He also presented several results concerning the Painleve type transitional asymptotics of Toeplitz determinants. Two talks were also given on random processes, by Pierre van Moerbeke and by Sandrine Péché. The lecture of Pierre van Moerbeke was devoted to nonintersecting Brownian motions leaving from and forced to return to one or several points. In his lecture, van Moerbeke described his very interesting recent results with Adler and Ferrari on the situation where two groups of particles just touch each other. Van Moerbeke has shown that a new limiting determinantal process appears near this tacnode. He also outlined the very elegant proof of these results based on a certain discretization technique followed by an orthogonal polynomial analysis on a circle. In her talk, Sandrine Péchédescribed her work demonstrating a profound connection of the distribution functions of the totally asymmetric exclusion process and of the last passage percolation to the KPZ -universality. This topic will be also a major theme in the December workshop. The bridge connecting RMT to statistical mechanics was featured in the lecture of Alice Guionnet mentioned above, and in the lecture of Pavel Bleher. The latter was devoted to the evaluation, with the help of the Riemann-Hilbert method, of the limiting behavior of the partition function of the six vertex model in different physical regimes. The results obtained by Bleher and his students are among the very few rigorous results available in the asymptotic analysis of non-free- fermionic models of statistical mechanics. A very interesting talk was given by Gerard Ben Arous. The talk dealt with some atypical aspects of the local eigenvalue statistics of the CUE and GUE ensembles. Specifically, he addressed the question of the asymptotic size and the limit laws of the smallest and largest gaps in the spectra of random matrices. The exact asymptotic behavior was evaluated for the both extreme cases. In addition, the limiting distribution law was found in the case of the smallest gap, and it is proven to be a Poisson law. These results appeared to be

Page 4 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

in a remarkable agreement with the numerical data concerning the analogous characteristics for the zeros of Riemann zeta function. Far reaching applications of random matrices were presented in the talks of Yang Chen and Nick Patterson. Yang Chen talked about perturbed Hankel determinants and their appearance in the theory of wireless communication. Nick Patterson in his lecture explained the role of random matrices in genetics. Patterson’s talk created a lot of excitement in the audience. Indeed, it was very interesting to see how the theoretical achievements in the field - such as the results of Baik, Ben-Arous, Péchéand Silverstein on the Tracy-Widom distributions in the theory of sample covariance matrices, are used in real ge- netical studies. “Baik-Ben Arous- Péché”,or BBP, theory featured prominently in Patterson’s talk. The reminder of the talks treated several other topics of interest. Integrable systems were the subject of the lecture given by Clarkson, although they, of course, were present in many other lectures during the workshop. One of the very challenging and important directions in random matrix theory - the multi- matrix model, was addressed in the lecture of A. Kuijlaars (and also in the previously described talk by Alice Guionnet) who focused on a key ingredient of the theory - the issue of vector equilibrium measures. The normal models were the topic of G. Akemann’s talk. An unexpected and very interesting use of random matrix techniques in the theory of scattering particles through a chaotic cavity was demonstrated in the talk given by F. Mezzadri.

Page 5 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Invited Speakers firstname lastname institutionname Gernot Akemann Brunel University Estelle Basor American Institute of Mathematics Gerard Ben Arous New York University Pavel Bleher Indiana University--Purdue University Gaëtan Borot Commissariat à l'Énergie Atomique (CEA) Yang Chen Imperial College, London Tom Claeys Université Catholique de Louvain Peter Clarkson University of Kent Philippe di Francesco Commissariat à l'Énergie Atomique (CEA) Persi Diaconis Stanford University Nicholas Ercolani University of Arizona Tamara Grava International School for Advanced Studies(SISSA/ISAS) Alice Guionnet Ecole Normale Supérieure de Lyon Igor Krasovsky Brunel University Arnoldus Kuijlaars Katholieke Universiteit Leuven Francesco Mezzadri University of Bristol Nicholas Patterson Broad Institute Sandrine Péché Université de Grenoble I (Joseph Fourier) Brian Rider University of Colorado Mariya Shcherbyna National Academy of Sciences of Ukraine Terence Tao University of California Pierre Van Moerbeke Université Catholique de Louvain Horng-Tzer Yau Harvard University

Page 6 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Schedule Monday September 13, 2010

09:25AM - 09:40AM Welcome Perturbed Hankel Determinants: Applications to the 09:40AM - 10:20AM Yang Chen Information Theory of MIMO Wireless Communications 10:20AM - 10:50AM Tea Geodesic distance in planar maps: from matrix models to 10:50AM - 11:30AM Philippe di Francesco trees Exact results in the Random Matrix Theory approach to 11:40AM - 12:20PM Francesco Mezzadri the theory of chaotic cavities 12:20PM - 02:15PM Lunch 02:15PM - 02:55PM Nicholas Patterson Genetics and large random matrices 02:55PM - 03:45PM Tea Beyond the Gaussian Universality Class (at UC Berkeley- 04:10PM - 05:10PM Ivan Corwin 60 Evans Hall)

Tuesday September 14, 2010 09:30AM - 10:10AM Alice Guionnet Planar algebras and the Potts model on random graphs 10:10AM - 10:40AM Tea Limiting distributions for TASEP, Last Passage 10:40AM - 11:20AM Sandrine Péché Percolation and a few words on universality in KPZ 11:30AM - 12:10PM Gerard Ben Arous TBD 12:10PM - 02:00PM Lunch 02:00PM - 02:40PM Nicholas Ercolani Cluster Expansions, Caustics and Counting Graphs Orthogonal and symplectic matrix models: universality 02:50PM - 03:30PM Mariya Shcherbyna and other properties 03:30PM - 04:00PM Tea 04:00PM - 04:40PM Brian Rider Beta ensembles on the line, edge universality

Page 7 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Wednesday September 15, 2010 Determinant expansions for perturbations of finite Toeplitz 09:30AM - 10:10AM Estelle Basor matrices 10:10AM - 10:40AM Tea 10:40AM - 11:20AM Igor Krasovsky Aspects of Toeplitz and Hankel determinants 11:30AM - 12:10PM Gernot Akemann Universality in Non-Hermitian RMT

Thursday September 16, 2010 Universality of Wigner random matrices via the four 09:30AM - 10:10AM Terence Tao moment theorem 10:10AM - 10:40AM Tea Universality of Random Matrices, Dyson Brownian 10:40AM - 11:20AM Horng-Tzer Yau Motion and Local Semicircle Law (Random) Tri-Diagonal, Doubly Stochastic Matrices, 11:30AM - 12:10PM Persi Diaconis Orthogonal Polynomials and Alternating Permutations 12:10PM - 02:30PM Lunch Maximal eigenvalue in beta ensembles: large deviations 02:30PM - 03:10PM Gaëtan BOROT and left tail of Tracy-Widom laws 03:10PM - 04:00PM Tea 04:00PM - 04:40PM Peter Clarkson Painleve Equations - Nonlinear Special Functions

Friday September 17, 2010 09:30AM - 10:10AM Pierre Van Moerbeke Dyson Brownian Motion and Critical Diffusions 10:10AM - 10:40AM Tea 10:40AM - 11:20AM Arnoldus Kuijlaars Vector equilibrium problem for the two-matrix model Universality Behviour of Solutions of Hamiltonian PDEs 11:30AM - 12:10PM Tamara Grava in Critical Regimes 12:10PM - 02:30PM Lunch 02:30PM - 03:10PM Tom Claeys Asymptotics for the Korteweg-de Vries equation and

Page 8 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

perturbations using Riemann-Hilbert methods 03:10PM - 04:00PM Tea Six-vertex model of statistical mechanics and random 04:00PM - 04:40PM Pavel Bleher matrix models

Page 9 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Officially Registered Participants firstname lastname institutionname Mark Adler Brandeis University Gernot Akemann Brunel University Tonci Antunovic University of California Antonio Auffinger New York University Jinho Baik University of Michigan Estelle Basor American Institute of Mathematics Gerard Ben Arous New York University Martin Bender Katholieke Universiteit Leuven Dan Betea California Institute of Technology Pavel Bleher Indiana University--Purdue University Alex Bloemendal University of Toronto Gaëtan Borot Commissariat à l'Énergie Atomique (CEA) Thomas Bothner Indiana University--Purdue University Lorna Brightmore Department of Mathematics, University of Bristol Robert Buckingham University of Cincinnati María-José Cantero University of Zaragoza Mireille Capitaine Centre National de la Recherche Scientifique (CNRS) Yang Chen Imperial College, London Margaret Cheney Rensselaer Polytechnic Institute Leonard Choup University of Alabama Leandro Cioletti University of Brasília Tom Claeys Université Catholique de Louvain Peter Clarkson University of Kent Ivan Corwin New York University Stephen Curran University of California Kim Dang Universität Zürich Alfredo Deaño Universidad Carlos III de Madrid Percy Deift New York University Amir Dembo Stanford University Philippe di Francesco Commissariat à l'Énergie Atomique (CEA) Persi Diaconis Stanford University Pierre Dueck University of California Maurice Duits California Institute of Technology Ioana Dumitriu University of Washington Nicholas Ercolani University of Arizona Avivith Fischmann Queen Mary and Westfield College

Page 10 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Peter Forrester University of Melbourne Jeff Geronimo Georgia Institute of Technology Math Department Dries Geudens Katholieke Universiteit Leuven Subhroshekhar Ghosh University of California Tamara Grava International School for Advanced Studies(SISSA/ISAS) Alice Guionnet Ecole Normale Supérieure de Lyon Adrien Hardy Katholieke Universiteit Leuven John Harnad CRM - Centre de Recherches Mathématiques Susan Holmes Stanford University Alexander Its Indiana University-Purdue University maria jivulescu Technical University of Timisoara Kurt Johansson KTH - Kungl Tekniska Högskolan Iain Johnstone Stanford University Vladislav Kargin Stanford University Rinat Kedem University of Illinois, Urbana-Champaign Kei Kobayashi The Institute of Statistical Mathematics Heinerich Kohler University Duisburg Essen Igor Krasovsky Brunel University Arnoldus Kuijlaars Katholieke Universiteit Leuven Ricky Kwok University of California Matti Lassas University of Helsinki Eunghyun Lee University of California Seung Yeop Lee California Institute of Technology Luen-Chau Li Pennsylvania State University Karl Liechty Indiana University--Purdue University Zhipeng Liu University of Michigan Milivoje Lukic California Institute of Technology Anna Lytova B.Verkin Institute for Low Temperature Physics and Engineering Shaun Maguire University of Hyderabad Mylene Maida Université de Paris XI (Paris-Sud) Camille Male UMPA - Ens lyon Andrei Martinez-Finkelsht Universidad de Almería Kenneth McLaughlin University of Arizona Ravi Menon University of California, San Diego Govind Menon Division of Applied Mathematics, Brown University Francesco Mezzadri University of Bristol Hartmut Monien Universität Bonn Alexey Nazarov Novosibirsk State University

Page 11 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Ion Nechita University of Ottawa Joel Nishimura Cornell University Jonathan Novak University of Waterloo Sean O'Rourke University of California Josh Oyoung University of California Nicholas Patterson Broad Institute Sandrine Péché Université de Grenoble I (Joseph Fourier) Christian Pfrang Brown University Mihail Poplavskyi National Academy of Sciences of Ukraine Miklos Racz University of California Emily Redelmeier Queens University David Renfrew University of California Brian Rider University of Colorado Dan Romik University of California Igor Rumanov University of California Tomohiro Sasamoto Chiba University Sylvia Serfaty Universite Pierre et Marie Curie Paris 6 Brigitte Servatius Worcester Polytechnic Institute Christopher Severs Reykjavik University Tatyana Shcherbina National Academy of Sciences of Ukraine Mariya Shcherbyna National Academy of Sciences of Ukraine Gregory Shinault University of California Christopher Shum University of Oregon Nicholas Simm University of Bristol Christopher Sinclair University of Oregon Alexander Soshnikov University of California David Steinberg Fiddletown Institute Kelli Talaska University of California Terence Tao University of California Craig Tracy University of California Benjamin Tsou University of California Gerónimo Uribe Bravo University of California Pierre Van Moerbeke Université Catholique de Louvain Vidya Venkateswaran California Institute of Technology Mirjana Vuletic Brown University MANAN VYAS Physical Research Laboratory Dong Wang University of Michigan Jacob White Arizona State University

Page 12 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Harold Widom University of California Lauren Williams University of California Pak Hin Wong Princeton University Manwah Wong Georgia Tech School of Mathematics Zhe Xu University of California Weijun Xu University of Oxford Maxim Yattselev University of Oregon Horng-Tzer Yau Harvard University Benjamin Young McGill University Anna Zemlyanova Texas A & M University James Zhao Stanford University

Page 13 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

Officially Registered Participant Information Participants 123

Gender 123 Male 73.17% 90 Female 23.58% 29 Declined to state 3.25% 4

Ethnicity* 126 White 64.29% 81 Asian 22.22% 28 Hispanic 1.59% 2 Pacific Islander 0.00% 0 Black 0.79% 1 Native American 0.00% 0 Declined to state 11.11% 14 * ethnicity specifications are not exclusive

Page 14 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 61 88% partially 6 9% no 0 0% no opinion 2 3%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 43 62% Satisfactory 26 38% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 16 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA Above satisfactory 50 72% Satisfactory 18 26% Not satisfactory 0 0% no opinion 1 1%

Additional comments on the topic presentation and organization Very nice throughout Many high level talks. Organization was excellent. It was a very interesting combination of different aspects of the theory and applications of random matrices, provided by intern ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 56 81% partially 13 19% no 0 0%

Did the workshop increase your interest in the subject? yes 68 99% partially 0 0% no 1 1%

Page 17 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA Was the workshop worth your time and effort? yes 68 99% partially 1 1% no 0 0%

Additional comments on your personal assessment I got a new information important for my personal research. Overall, the workshop was very useful to estimulate research in the area of random matrix theory and applications Workshop was very valuable ...

Venue

Your overall experience at MSRI 1 - Above satisfactory 57 83% 2 11 16% 3 0 0% 4 1 1% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff

Page 18 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA 1 - Above satisfactory 48 70% 2 20 29% 3 0 0% 4 0 0% 5 - Not satisfactory 1 1%

Above satisfactoryNot satisfactory

Page 19 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA

The physical surroundings 1 - Above satisfactory 55 80% 2 13 19% 3 0 0% 4 0 0% 5 - Not satisfactory 1 1%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 - Above satisfactory 8 12% 2 26 38% 3 22 32% 4 11 16% 5 - Not satisfactory 2 3%

Above satisfactoryNot satisfactory

Additional comments on the venue MSRI staff was very helpful. Participants generally felt hungry during the conference, especially in the afternoon. A lot of us went back to purchase lunch after having the tiny sandwich but the vend ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. All the staff members were extremely helpful. Thank you for organizing such a great conference! Organize travel by participants to good non-expensive restaurants which are available in Berkeley. This ...

Page 20 of 21 Random Matrix Theory and Its Applications I, September 13 to 19, 2010 at MSRI, Berkeley, CA Number of daily responses

Page 21 of 21

Connections for Women: An Introduction to Random Matrices September 20 to 21, 2010 MSRI, Berkeley, CA, USA

Organizers: Estelle Basor (American Institute of Mathematics, Palo Alto) Alice Guionnet* (Ecole Normale Supérieure de Lyon) Irina Nenciu (University of Illinois at Chicago)

Parent Program: Statistical Challenges for Meta-Analysis of Medical and Health-Policy Data Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Report on the ‘Connection for women: workshop on random matrices’

September 20-21, 2010

Organizers

• Estelle Basor, American Institute of Mathematics, Palo Alto • Alice Guionnet, ENS Lyon • Irina Nenciu, MSCS, UIC, Chicago

One of the aims of this workshop was to present basic notions from random matrix theory, with a particular focus on providing background material so that all participants can interact successfully with more experienced and senior researchers involved in the program. Many of the senior participants are experts in one area of random matrix theory and have less familiarity with techniques and results from other related topics. This workshop broadened the knowledge of all participants so that they could interact with all aspects of the parent program. Random Matrix Theory (RMT) started in the twenties with the work of Wishart in multivariate analysis. It developed in theoretical physics after Wigner and Dyson used random matrices as an approximation of the Hamiltonian of highly excited nuclei. After the work of ’t Hooft in the seventies, it became a central tool to tackle QCD, string theory and hard combinatorial questions. At about the same time, Montgomery conjectured that the non trivial zeroes of the Riemann Zeta function are related with the eigenvalues of large random matrices. Since that time an extraordinary variety of mathematical, physical and engineering systems have been related with RMT; it has emerged as an interdisciplinary scientific activity par excellence. Since random matrix theory has been found to be such an important model for so many topics in mathematics and physics we wanted to highlight as much of the basic areas as possible. Topics covered in this workshop included fundamental problems in random matrices. We had eight one hour talks, which provided background materials in active research areas. More precisely, the themes which were represented were universality questions (Sandrine Péché),connections with integrable systems and PDE’s (Tamara Grava and Irina Nenciu) and with large random graphs

Page 2 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

(Ioana Dumitriu and Maria Scherbina), non-normal matrices (Alice Guionnet) and the effect of finite rank perturbation on the spectrum of random matrices (Mireille Capitaine and Mylene Maida). Mireille Capitaine and Alice Guionnet talks both emphasized the use of free probability to analyze the spectrum of random matrices. We had four talks each day with ample time for discussion between the talks. The talks were well attended by the participants in the parent program and the participants of the first workshop. Many of the participants of the connection workshop were able to come to MSRI a few days or even a week before the connection workshop and thus also attended the week long introductory workshop. We organized a panel session on the first evening, which discussed the role and obstacles facing women in mathematica careers. The dinner on the first evening was very successful with more than twenty women attending and many open discussions.

Page 3 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Invited Speakers firstname lastname institutionname Mireille Capitaine Centre National de la Recherche Scientifique (CNRS) Ioana Dumitriu University of Washington Tamara Grava International School for Advanced Studies (SISSA/ISAS) Alice Guionnet Ecole Normale Supérieure de Lyon Mylene Maida Université de Paris XI (Paris-Sud) Irina Nenciu University of Illinois Sandrine Péché Université de Grenoble I (Joseph Fourier) Mariya Shcherbyna National Academy of Sciences of Ukraine

Page 4 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Schedule Monday September 20, 2010 09:25AM - Welcome 09:40AM 09:40AM - Universality in the bulk of the spectrum for Hermitian random Sandrine Péché 10:40AM matrices 10:40AM - Tea 11:10AM 11:10AM - Irina Nenciu TBD 12:10PM 12:10PM - Lunch 02:00PM 02:00PM - Universality results for hamiltonian perrturbations of Tamara Grava 03:00PM Hamiltonian PDEs: the 2 component case 03:00PM - Tea 03:30PM 03:30PM - Fluctuations and Large Deviations for Extreme Eigenvalues of Mylene Maida 04:30PM Deformed Random Matrices 04:35PM - Panel (Commons) 05:45PM Tuesday September 21, 2010 09:30AM - Sparse regular random graphs: spectral density and eigenvectors Ioana Dumitriu 10:30AM 10:30AM - Tea 11:00AM 11:00AM - Alice Guionnet The Single Ring Theorem 12:00PM 12:00PM - Lunch 02:00PM 02:00PM - Free convolution with a semi-circular distribution and Mireille Capitaine 03:00PM eigenvalues of spiked deformations of Wigner matrices 03:00PM - Tea 03:30PM 03:30PM - Central limit theorem for linear eigenvalue statistics of diluted Mariya Shcherbyna 04:30PM random matrices

Page 5 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Officially Registered Participants firstname lastname institutionname Jinho Baik University of Michigan Estelle Basor American Institute of Mathematics Dan Betea California Institute of Technology Tristram Bogart University of Washington Lorna Brightmore Department of Mathematics, University of Bristol Branimir Cacic California Institute of Technology, Department of Mathematics Mireille Capitaine Centre National de la Recherche Scientifique (CNRS) Yang Chen Imperial College, London Ivan Corwin New York University Kim Dang Universität Zürich Alfredo Deaño Universidad Carlos III de Madrid Catherine Donati Centre National de la Recherche Scientifique (CNRS) Ioana Dumitriu University of Washington Nicholas Ercolani University of Arizona Avivith Fischmann Queen Mary and Westfield College dalit gafni the college of management academic studies Dries Geudens Katholieke Universiteit Leuven Tamara Grava International School for Advanced Studies (SISSA/ISAS) Alice Guionnet Ecole Normale Supérieure de Lyon Adrien Hardy Katholieke Universiteit Leuven Joanna Hutchinson University of Bristol Maria Jivulescu Technical University of Timisoara Anna Kononova Baltic State Technical University Arnoldus Kuijlaars Katholieke Universiteit Leuven Anna Lytova B.Verkin Institute for Low Temperature Physics and Engineering Mylene Maida Université de Paris XI (Paris-Sud) Camille Male UMPA - Ens lyon Zeinab Mansour King Saud University Fatemeh Mohammadi Ferdowsi University of Mashhad Irina Nenciu University of Illinois Josh Oyoung University of California Sandrine Péché Université de Grenoble I (Joseph Fourier) Carmelita Ragasa University of the East Manila Emily Redelmeier Queens University David Renfrew University of California Brigitte Servatius Worcester Polytechnic Institute

Page 6 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Tatyana Shcherbina National Academy of Sciences of Ukraine Mariya Shcherbyna National Academy of Sciences of Ukraine Nicholas Simm University of Bristol Vidya Venkateswaran California Institute of Technology Mirjana Vuletic Brown University MANAN VYAS Physical Research Laboratory Zhen Wei University of Virginia Jacob White Arizona State University Manwah Wong Georgia Tech School of Mathematics Zhe Xu University of California Benjamin Young McGill University Anna Zemlyanova Texas A & M University

Page 7 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 48

Gender 48 Male 35.42% 17 Female 60.42% 29 Declined to state 4.17% 2

Ethnicity* 49 White 67.35% 33 Asian 24.49% 12 Hispanic 2.04% 1 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 6.12% 3 * ethnicity specifications are not exclusive

Page 8 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 30 97% partially 1 3% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 20 65% Satisfactory 11 35% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 10 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA Above satisfactory 21 68% Satisfactory 9 29% Not satisfactory 0 0% no opinion 1 3%

Additional comments on the topic presentation and organization Very nice format The topics were interesting. It would be better if some basic introduction to the topics be given before all the speakers presented their paper. The introduction may also include the ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 22 71% partially 8 26% no 1 3%

Did the workshop increase your interest in the subject?

Page 11 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA yes 29 94% partially 2 6% no 0 0%

Was the workshop worth your time and effort? yes 30 97% partially 1 3% no 0 0%

Additional comments on your personal assessment for my phd-thesis, this workshop was a great inspiration

Venue

Your overall experience at MSRI 1 - Above satisfactory 26 84% 2 3 10% 3 2 6% 4 0 0% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Page 12 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA The assistance provided by MSRI staff 1 - Above satisfactory 24 77% 2 7 23% 3 0 0% 4 0 0% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The physical surroundings 1 - Above satisfactory 26 84% 2 4 13% 3 1 3% 4 0 0% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 - Above satisfactory 7 23% 2 11 35% 3 11 35% 4 2 6% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Additional comments on the venue Auditorium projector screen was too small for the room, and was difficult to see from further back or the sides.

Thank you for completing this survey

Page 13 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. Would have liked more time between the end of the first day and the conference meal. I think enough time should be left so people don't need to arrive with all their notes and things from the day!

Number of daily responses

Page 14 of 15 Connections for Women: An Introduction to Random Matrices, September 20 to 21, 2010 at MSRI, Berkeley, CA, USA

Connections for Women: An introduction to Random Matrices Additional Survey Responses

Additional comments on the topic presentation and organization

 Very nice format  It would be better if some basic introduction to the topics be given before all the speakers presented their paper. The introduction may also include the background of the speakers.  one hour talks and introductions are very convenient

Additional comments on the venue

 Auditorium projector screen was too small for the room and was difficult to see from further back or the sides

Additional comments on your personal assessment

 For my phd-thesis, this workshop was a great inspiration

We welcome any additional comments or suggestions you may have to improve the overall experience for future participants

 Would have liked more time between the end of the first day and the conference meal. I think enough time should be left so people don’t need to arrive with all their notes and things from the day!

Page 15 of 15

Random Matrix Theory and its Applications II December 6 to 10, 2010 MSRI, Berkeley, CA, USA

Organizers: Alexei Borodin* (California Institute of Technology) Percy Deift (Courant Institute of Mathematical Sciences) Alice Guionnet (Ecole Normale Supérieure de Lyon) Pierre van Moerbeke (Universite Catholique de Louvain and Brandeis University) Craig A.Tracy (University of California, Davis) Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

January 31, 2011

Report on the MSRI workshop “Random Matrix Theory and Its Applications II” December 6 - 10, 2010

Organizers

• Alexei Borodin (Caltech and MIT) • Percy Deift (Courant Institute) • Alice Guionnet (Ecole Normale Superieure de Lyon) • Pierre van Moerbeke (Universite Catholique de Louvain and Brandeis) • Craig Tracy (University of California, Davis)

1. Scientiﬁc description

In this final workshop of the program the main emphasis was on various probabilistic and mathematical physics models that at first sight seem fairly distant to Random Matrix Theory (RMT), but end up being (often miracu- lously) solvable by RMT methods. One of the most prominent examples is the decription of the large time nonequilibrium fluctuations in the totally asymmetric simple exclusion process (TASEP) with step initial condition by Johansson 12 years ago. Johansson’s result was part of a very active development approximately 10 years ago of the domain that one could call “discrete RMT”, where one considers discrete probabilistic models that are very reminiscent of the RMT ones but with “eigenvalues” confined to a lattice. The origins of the models are very diverse - from interacting particle systems to tiling models to representation theory. In recent years discrete RMT has gained a lot of new momentum. Starting from 2005, Sasamoto and collaborators developed a new combinatorial approach that allowed to extend results from earlier works to new classes of initial conditions and lead to the introduction of the Airy1 process. Starting from 2007 Tracy and Widom developed a new method of analysis of the asymmetric simple exclusion process (ASEP), and that allowed Sasamoto-Spohn and Amir-Corwin- Quastel to rigorously analyze solutions to the celebrated Kardar-Parisi-Zhang (KPZ) equation. Seppalainen and collaborators, also starting from 2007, found a new way of establishing t1/3 scaling exponent in TASEP-like models purely probabilistically, without appealing to integrable methods. Over the last 2-3 years the domain has become very hot again. Another major topic of the workshop was the so-called general β ensembles. It is well known since the beginnings of RMT that full random matrix models naturally lead to measures of log-gas type with three prescribed values of the temperature. These three values are usually encoded by a parameter β = 1, 2, 4, and they correspond to the three possibilities of the base (skew)-field of reals, complex numbers, or quaternions. It is very natural to try to extend random matrix techniques to the log-gas with an arbitrary (positive) value of

Page 2 of 15 Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

β, and this problem remained a major challenge until approximately five years ago. Following the pioneering work of Dumitriu-Edelman and Edelman-Sutton, Ramirez-Rider-Virag in 2006 were able to characterize the edge scaling limit of the log-gas with an arbitrary β as eigenvalues of a stochastic Schroedinger operator. Since then the subject has been actively developing. The third important topic discussed in the workshop was the random tiling models. While the connections between random tiling models and RMT became apparent during the birth of “discrete RMT” 12 years ago, the progress on random tilings had a different trajectory. Through the works of Okounkov and collaborators the subject got related to enumerative algebraic geometry (Hur- witz numbers, Gromov-Witten and Donaldson-Thomas invariants) and further to mirror symmetry and string theory. In a different direction, Kenyon and collaborators developed an exciting area of “random surfaces” that are often in bijection with a suitable tiling problem. The subject remains very active and it attracts interest of researchers from many different domains. In addition, RMT becomes increasingly important in statistics and signal processing, and those developments were also represented in the workshop.

2. Highlights

The largest portion of the talks was dedicated to the one-dimensional growth models. H. Widom gave an in-depth presentation of their method with C. Tracy that allowed to produce analyzable exact formulas for the transition probabilities of the ASEP. H. Spohn, T. Sasamoto, and J. Quastel spoke about approaching KPZ equation as a limiting version of the weakly asymmetric simple exclusion process. P. Ferrari spoke on similarities and differences of the Dyson Brown- ian motion and one and two-dimensional interacting particle systems. T. Sep- palainen explained the probabilistic approach to the KPZ scaling exponents. L. Williams gave a presentation of the combinatorial approach to the equilibrium ASEP on an open interval. Remarkably, the result has strong connections to the Askey-Wilson classical orthogonal polynomials that are at the top of the Askey scheme of orthogonal polynomials of hypergeometric type. Last but not least, N. O’Connell explained a connection between a finite temperature directed polymer model and solutions of the quantum Toda Lattice (TASEP may be viewed as an infinite temperature directed polymer) The exposition of so many different viepoints lead to many fruitful discussions. The icing on the cake was a talk by K. Takeuchi who explained how the universal Tracy-Widom distributions of RMT appear in a physical experiment of crystal growth. This work caused a lot of excitement among the participants. The general β ensembles were represented by three talks. B. Virag (in a joint work with A. Bloemendal) managed to apply the techniques of the stochastic Schroedinger operators to solve the β = 1 problem of the phase transition in the largest eigenvalue as the random matrix gets perturbed by a finite rank deformation (“spiked” model). This solved a conjectured of Baik-Ben Arous- Peche from 2005. I. Dumitru and B. Valko spoke about exciting new results that are more intrinsic. Regarding random tiling models, there were two talks. A. Okounkov presented his most recent work on connecting lozenge tilings to objects in noncommutative algebraic geometry. He also showed that moving the walls of the tiled domains could be viewed as a quantum integrable systems and can further be related to the classical (nonlinear ordinary differential) Painleve equations. N. Reshetikhin gave a general recipe of connecting general random tiling models

2 Page 3 of 15 Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

to nonintersecting paths (an approach that proved to be extremely useful in the past), and also outlined a variety of problems related to the six-vertex model that remain unsolved. There were a number of other talks by leading researchers: D. Lubinsky spoke about his pioneering approach to universality questions in RMT, N. Ma- karov and P. Wiegmann discussed random matrices with complex eigenvalues and their relation to classical complex analysis and conformal ﬁeld theory, N. El Karoui described statistical applications of RMT, and K. Solna explained how RMT is used in the problem of signal detection. All the talks were well attended, with many young people in the audience, and the level of hallway discussions was very high. There was an overall feeling that RMT keeps expanding and excitement on the amount of new mathematical ideas, as well as applications, that it attracts.

3 Page 4 of 15 Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Mark Adler Brandeis University Ioana Dumitriu University of Washington Alan Edelman Massachusetts Institute of Technology Noureddine El Karoui Stanford University Patrik Ferrari Bonn University Alice Guionnet École Normale Supérieure de Lyon Doron Lubinsky Georgia Institute of Technology Nikolai Makarov California Institute of Technology Neil O'Connell University of Warwick Andrei Okounkov Columbia University Jeremy Quastel University of Toronto Nicolai Reshetikhin University of California, Berkeley Tomohiro Sasamoto Chiba University Timo Seppalainen University of Wisconsin Knut Solna University of California, Berkeley Herbert Spohn Technische Universität München Kazumasa Takeuchi Commissariat à l'Énergie Atomique Benedek Valko University of Wisconsin Balint Virag University of Toronto Harold Widom University of California, Berkeley Paul Wiegmann University of Chicago Lauren Williams University of California, Berkeley Nicholas Witte St. Norbert College

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Schedule Monday, December 06, 2010 Simons Welcome 8:30AM - 8:45AM Auditorium Simons The Dyson Brownian Minor Process and 8:45AM - 9:45AM Mark Adler Auditorium Consecutive Minors 9:45AM - 10:15AM Tea Simons 10:15AM - 11:15AM Harold Widom A Useful Integral Representation in ASEP Auditorium Simons The KPZ Equation: Lattice Discretizations 11:30AM - 12:30PM Herbert Spohn Auditorium and Replica 12:30PM - 2:00PM Lunch Height Distributions in One-Dimensional Simons 2:00PM - 3:00PM Tomohiro Sasamoto Surface Growth: from ASEP to KPZ Auditorium Equation 3:00PM - 3:30PM Tea 4:10PM - 5:00PM UC Berkeley Alice Guionnet Asymptotics of Random Matrices Tuesday, December 07, 2010 Simons TASEP and Gaussian Ensembles: Analogies 9:00AM - 10:00AM Patrik Ferrari Auditorium and Differences 10:00AM - 10:30AM Tea Simons 10:30AM - 11:30AM Jeremy Quastel The Continuum Random Polymer and KPZ Auditorium Tracy-Widom Distributions in Experiment: Simons 11:30AM - 12:30PM Kazumasa Takeuchi Evidence in Growing Interfaces of Liquid Auditorium Crystal Turbulence 12:30PM - 2:30PM Lunch Simons Scaling Exponents for Certain 1+1- 2:30PM - 3:30PM Timo Seppalainen Auditorium Dimensional Directed Polymers 3:30PM - 4:00PM Tea Simons A Combinatorial Approach to the 4:00PM - 5:00PM Lauren Williams Auditorium Asymmetric Exclusion Process Reception 5:00PM - 6:30PM

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Wednesday, December 08, 2010 Simons Universality Limits for Random Matrices via 9:00AM - 10:00AM Doron Lubinsky Auditorium Classical Complex Analysis 10:00AM - 10:30AM Tea Simons Emergent Conformal Invariance in Selberg- 10:30AM - 11:30AM Paul Wiegmann Auditorium Dyson's Integrals Simons TBA 11:30AM - 12:30PM Nikolai Makarov Auditorium Thursday, December 09, 2010 Simons Finite-Rank Pertutbations of Real Random 9:00AM - 10:00AM Balint Virag Auditorium Matrices 10:00AM - 10:30AM Tea Simons 10:30AM - 11:30AM Andrei Okounkov Noncommutative Geometry and Painlevé Auditorium Simons 11:30AM - 12:30PM Nicolai Reshetikhin On Height Functions Auditorium 12:30PM - 2:30PM Lunch Simons Target Detection and Localization in the 2:30PM - 3:30PM Knut Solna Auditorium Presence of Noise 3:30PM - 4:00PM Tea Simons Directed Polymers and the Quantum Toda 4:00PM - 5:00PM Neil O'Connell Auditorium Lattice Friday, December 10, 2010 What are the Eigenvalues of a Sum of Non- Simons 9:00AM - 10:00AM Alan Edelman Commuting Random Symmetric Matrices? : Auditorium A "Quantum Information" inspired Answer. 10:00AM - 10:30AM Tea Simons 10:30AM - 11:30AM Ioana Dumitriu Auditorium Global Fluctuations for β-Jacobi Ensembles Simons 11:30AM - 12:30PM Nicholas Witte λ Expansions of Fredholm Determinants and Auditorium the Borodin-Okounkov Identity 12:30PM - 2:00PM Lunch Simons 2:00PM - 3:00PM Benedek Valko Scaling Limits of Beta Ensembles Auditorium 3:00PM - 3:30PM Tea Simons Noureddine El Some Remarks on Random Matrix Theory 3:30PM - 4:30PM Auditorium Karoui and Statistics

Page 7 of 15 Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Mark Adler Brandeis University Antonio Auffinger New York University Arvind Ayyer University of California Jinho Baik Princeton University Gerard Ben Arous New York University Martin Bender Katholieke Universiteit Leuven Dan Betea California Institute of Technology Pavel Bleher Indiana University--Purdue University Natasa Blitvic Massachusetts Institute of Technology Alex Bloemendal University of Toronto Leonid Bogachev University of Leeds Robert Buckingham University of Cincinnati Mattia Cafasso University of Montreal Isabelle Camilier Stanford University Leonard Choup University of Alabama Ivan Corwin New York University Kim Dang Universität Zürich Alfredo Deaño Universidad Carlos III de Madrid Percy Deift New York University Steven Delvaux University of Leuven Amir Dembo Stanford University Maurice Duits California Institute of Technology Ioana Dumitriu University of Washington Alan Edelman Massachusetts Institute of Technology Torsten Ehrhardt University of California, Berkeley Noureddine El Karoui Stanford University Nicholas Ercolani University of Arizona Patrik Ferrari Bonn University Subhroshekhar Ghosh University of California, Berkeley Alice Guionnet École Normale Supérieure de Lyon John Harnad Centre de Recherches Mathématiques Olga Holtz University of California, Berkeley Takashi Imamura Research Center for Advanced Science and Technology Alexander Its Indiana University--Purdue University Tobias Johnson University of Washington Iain Johnstone Stanford University Liza Jones University of Bristol Vladislav Kargin Stanford University Kei Kobayashi The Institute of Statistical Mathematics Robert Korsan n/a Thomas Kriecherbauer New York University, Courant Institute Arnoldus Kuijlaars Katholieke Universiteit Leuven Ricky Kwok University of California Michel Lapidus University of California Eunghyun Lee University of California Seung Yeop Lee California Institute of Technology Danning Li University of Minnesota Twin Cities Luen-Chau Li Pennsylvania State University Karl Liechty Indiana University--Purdue University Zhipeng Liu University of Michigan Doron Lubinsky Georgia Institute of Technology Milivoje Lukic California Institute of Technology

Page 8 of 15 Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

First Name Last Name Current Institution Nikolai Makarov California Institute of Technology Camille Male UMPA - Ens lyon Anthony Mays University of Melbourne Ken McLaughlin University of Arizona Anthony Metcalfe Royal Institute of Technology (KTH) Sevak Mkrtchyan Rice University Fatemeh Mohammadi Ferdowsi University of Mashhad Hajime Nagoya Kobe University Stephen Ng University of California, Davis Eric Nordenstam Université Catholique de Louvain Jonathan Novak University of Waterloo Neil O'Connell University of Warwick Andrei Okounkov Columbia University Sean O'Rourke University of California Janosch Ortmann University of Warwick Josh Oyoung University of California Elliot Paquette University of Washington Christian Pfrang Brown University Jeremy Quastel University of Toronto Miklos Racz University of California, Berkeley Anand Rajagopalan University of California, Los Angeles Emily Redelmeier Queen's University David Renfrew University of California, Berkeley Nicolai Reshetikhin University of California, Berkeley Ilan Roth University of California, Berkeley Igor Rumanov University of California, Berkeley Tomohiro Sasamoto Chiba University Timo Seppalainen University of Wisconsin Gregory Shinault University of California, Berkeley Christopher Sinclair University of Oregon Knut Solna University of California, Berkeley Alexander Soshnikov University of California, Berkeley Herbert Spohn Technische Universität München Will Stanton University of Colorado Kazumasa Takeuchi Commissariat à l'Énergie Atomique Kelli Talaska University of California, Berkeley Craig Tracy University of California, Berkeley Benedek Valko University of Wisconsin Balint Virag University of Toronto Mirjana Vuletic Brown University Vladislav Vysotsky Arizona State University Dong Wang University of Michigan Jacob White Arizona State University Harold Widom University of California, Berkeley Paul Wiegmann University of Chicago Lauren Williams University of California, Berkeley Nicholas Witte St. Norbert College Maxim Yattselev University of Oregon Benjamin Young McGill University Anna Zemlyanova Texas A & M University

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Officially Registered Participant Information Participants 102

Gender 102 Male 79.41% 81 Female 12.75% 13 Declined to state 7.84% 8

Ethnicity* 104 White 54.81% 57 Asian 20.19% 21 Hispanic 0.00% 0 Pacific Islander 0.00% 0 Black 0.96% 1 Native American 0.00% 0 Declined to state 24.04% 25 * ethnicity specifications are not exclusive

Page 10 of 15 Edit form - [ Random Matrix Theory and its Applications II - Participant ... https://docs.google.com/spreadsheet/gform?key=0AvkL2Nf5_6SsdFAyN...

Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 45 90% partially 5 10% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 30 60% Satisfactory 20 40% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion? Above satisfactory 26 52% Satisfactory 24 48% Not satisfactory 0 0% no opinion 0 0%

Page 12 of 15

1 of 4 4/23/2012 11:54 AM Edit form - [ Random Matrix Theory and its Applications II - Participant ... https://docs.google.com/spreadsheet/gform?key=0AvkL2Nf5_6SsdFAyN...

Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA Additional comments on the topic presentation and organization Excellent workshop! A full hour was perhaps too much for some talks that focused on a single model/question rather than presenting a broader picture. On the other it would be difficult for the organ ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 34 68% partially 15 30% no 1 2%

Did the workshop increase your interest in the subject? yes 43 86% partially 7 14% no 0 0%

Was the workshop worth your time and effort? yes 47 94% partially 3 6% no 0 0%

Page 13 of 15

2 of 4 4/23/2012 11:54 AM Edit form - [ Random Matrix Theory and its Applications II - Participant ... https://docs.google.com/spreadsheet/gform?key=0AvkL2Nf5_6SsdFAyN...

Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA Additional comments on your personal assessment Some of the speakers were wonderful and some were atrocious. I wish there were some way to give feedback to individual speakers so that they knew how much (or how little, in some cases) they were b ...

Venue

Your overall experience at MSRI 1 -Above satisfactory 38 76% 2 7 14% 3 0 0% 4 4 8% 5 -Not satisfactory 1 2%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff 1 -Above satisfactory 34 68% 2 12 24% 3 0 0% 4 1 2% 5 -Not satisfactory 3 6%

Above satisfactoryNot satisfactory

The physical surroundings 1 -Above satisfactory 37 74% 2 8 16% 3 1 2% 4 1 2% 5 -Not satisfactory 3 6%

Above satisfactoryNot satisfactory

Page 14 of 15

3 of 4 4/23/2012 11:54 AM Edit form - [ Random Matrix Theory and its Applications II - Participant ... https://docs.google.com/spreadsheet/gform?key=0AvkL2Nf5_6SsdFAyN...

Random Matrix Theory and its Applications II December 6 to 10, 2010 at MSRI, Berkeley, CA, USA The food provided during the workshop 1 -Above satisfactory 8 16% 2 18 36% 3 15 30% 4 6 12% 5 -Not satisfactory 3 6%

Above satisfactoryNot satisfactory

Additional comments on the venue The food on the last two days was better than the first few days. Only minus point is the lunch. That could use some improvement. Otherwise, very satisfactory. The cheese cakes on Monday raised expec ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. In the Rose garden inn you recommend, networking is not usable in each room and one has to go to the lobby. It was pretty inconvenient. Rose Garden Inn is a good suggestion for a hotel because they ...

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Page 15 of 15

4 of 4 4/23/2012 11:54 AM

Connections for Women: Inverse Problems and Applications August 19 to August 20, 2010 MSRI, Berkeley, CA, USA

Organizers: Tanya Christiansen (University of Missouri, Columbia) Alison Malcolm (Massachusetts Institute of Technology) Shari Moskow (Drexel University) Chrysoula Tsogka (University of Crete) Gunther Uhlmann* (University of Washington)

Parent Program: Inverse Problems and Applications Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Report Connection for Women Workshop, August 19-20, 2010

Organizing Committee: Tanya Christiansen (University of Columbia, Missouri) Alison Malcolm, (MIT) Shari Moskow (Drexel University) Chrysoula Tsogka (University of Crete) Gunther Uhlmann, chair (U. Washington and UC Irvine)

Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth’s substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The workshop consisted of four minicourses of 2 hours each that gave an introduction to several of the topics discussed in the Introductory Workshop the following week as well as topics that will be discussed during the Fall semester. A brief description of each minicourse follows.

• An Introduction to Microlocal Analysis Lecturer: Tanya Christiansen (U. of Missouri, Columbia) Microlocal analysis is useful in understanding solutions of differential equations. Pseudodif- ferential operators arise, for example, in inverting elliptic differential equations. The lecturer introduced pseudodifferential operators and their mapping properties. The notion of “wave front set” of a function was introduced and it was shown that is very helpful in describing its singularities. • An Introduction To Seismic Imaging Lecturer: Alison Malcolm (MIT) This course gave a broad overview of seismic imaging techniques, highlighting their underlying relationships to imaging in other fields (e.g. radar and ultrasound). We will begin with the Generalized Radon Transform, progress to one-way methods using a microlocal splitting of the wave equation into up- and down-going waves, and finish with a discussion of so-called reverse- time migration in which the full wave equation is run backwards in time to form an image. The approximations underlying each method and their relative importance were discussed as well as extensions beyond single-scattering. • An Introduction to Asymptotic Expansions for Small Inhomogeneities in EIT and Related Problems Lecturer: Sharil Moskow (Drexel U.) In this course the lecturer explained the basic tools and derivation of series expansions for potential data in the presence of small volume inhomogeneities which are different from a smooth background conductivity. We explain what properties can be recovered from the series terms and give a few ideas about how these expansions can be used to do inversion. Lecturer: Chrysoula Tsogka (U. of Crete)

Page 2 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

In this course the lecturer considered the problem of arrayimaging in cluttered media, in regimes with signiﬁcant multiple scatteringof the waves by the inhomogeneities.In such scat- teringregimes, the recorded traces at the array have long and noisy codasand classic imaging methods give unstable results.Statistically stable imaging methodologies for imaging in such regimes were discussed.

Page 3 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Invited Speakers firstname lastname institutionname Tanya Christiansen University of Missouri Alison Malcolm MIT Shari Moskow Drexel University Chrysoula Tsogka University of Crete

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Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Schedule Thursday August 19, 2010 09:30AM - 10:30AM Tanya Christiansen Introduction to Microlocal Analysis I 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Tanya Christiansen Introduction to Microlocal Analysis II 12:00PM - 02:00PM Lunch An Introduction to Asymptotic Expansions for Small 02:00PM - 03:00PM Shari Moskow Inhomogeneities in EIT and Related Problems I 03:00PM - 03:30PM Tea 03:30PM - 04:30PM Chrysoula Tsogka Coherent Imaging in Random Media I 04:45PM - 05:45PM Panel (Commons) Friday, August 20, 2010 09:30AM - 10:30AM Chrysoula Tsogka Coherent Imaging in Random Media II 10:30AM - 11:00AM Tea An Introduction to Asymptotic Expansions for Small 11:00AM - 12:00PM Shari Moskow Inhomogeneities in EIT and Related Problems II 12:00PM - 02:00PM Lunch 02:00PM - 03:00PM Alison Malcolm Introduction to Seismic Imaging I 03:00PM - 03:30PM Tea 03:30PM - 04:30PM Alison Malcolm Introduction to Seismic Imaging II

Page 5 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Officially Registered Participants firstname lastname institutionname Gaik Ambartsoumian University of Texas Jennifer Anderson University of Texas Elena Beretta Universita' La Sapienza Liliana Borcea Rice University Fioralba Cakoni Tirana University Margaret Cheney Rensselaer Polytechnic Institute Daeshik Choi University of Washington Tanya Christiansen University of Missouri David Colton University of Delaware Mimi Dai University of California David Dos Santos Ferreira Université de Paris 13 (Nord) Ricardo Gallardo Rice University Fernando Guevara Vasquez University of Utah Sarah Hamilton Colorado State University Pilar Herreros Universität Münster Hamid Hezari Massachusetts Institute of Technology Yulia Hristova Institute for Mathematics and its Applications Natali Hritonenko Prairie View A&M University Mark Hubenthal University of Washington ilker kocyigit University of Washington Ru-Yu Lai University of Washington Peter Ledochowitsch University of California Jennifer Lopez Department of Defense Priscilla Macansantos University of the Philippines, Baguio City Alison Malcolm MIT Graeme Milton University of Utah Shari Moskow Drexel University Linh Nguyen Texas A & M University Heather Palmeri Rensselaer Polytechnic Institute Lee Patrolia University of Washington Leonid Pestov Ugra Institute of Information Technologies Valter Pohjola University of Helsinki Hai-Hua Qin University of Delaware Renate Quehenberger University of applied Arts Vienna Vladimir Sharafutdinov Siberian Branch Russian Academy of Sciences Ashley Thomas Rensselaer Polytechnic Institute Justin Tittelfitz University of Washington Nilifer Topsakal University of Texas, Arlington Chrysoula Tsogka University of Crete Gunther Uhlmann University of Washington Jue Wang Union College--Union University Tegan Webster Rensselaer Polytechnic Institute Zhen Wei University of Virginia Ting Zhou Unversity of Washington

Page 6 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Officially Registered Participant Information Participants 44

Gender 44 Male 38.64% 17 Female 61.36% 27 Declined to State 0.00% 0

Ethnicity* 44 White 65.91% 29 Asian 20.45% 9 Hispanic 11.36% 5 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to State 2.27% 1 * ethnicity specifications are not exclusive

Page 7 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

responses

Summary See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 18 86% partially 3 14% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 14 67% Satisfactory 6 29% Not satisfactory 0 0% no opinion 1 5%

Was there adequate time between lectures for discussion?

Page 9 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Above satisfactory 14 67% Satisfactory 7 33% Not satisfactory 0 0% no opinion 0 0%

Additional comments on the topic presentation and organization All the lecturers were amazing! I look forward to getting material on the lectures. The presenters were very well prepared and they gave interesting lectures. very proficient it was very good experien ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 14 67% partially 7 33% no 0 0%

Did the workshop increase your interest in the subject? yes 20 95% partially 0 0% no 1 5%

Page 10 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

Was the workshop worth your time and effort? yes 19 90% partially 2 10% no 0 0%

Additional comments on your personal assessment I am interested in reading up more on the recent results in this research area. I believe it is not inaccessible even for those who have not done a lot of work in the research area very inspiring I wa ...

Venue

Your overall experience at MSRI 1 - Above satisfactory 16 76% 2 3 14% 3 1 5% 4 1 5% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff

Page 11 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

1 - Above satisfactory 14 67% 2 5 24% 3 1 5% 4 1 5% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The physical surroundings 1 - Above satisfactory 19 90% 2 0 0% 3 1 5% 4 0 0% 5 - Not satisfactory 1 5%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 - Above satisfactory 8 38% 2 7 33% 3 4 19% 4 2 10% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Additional comments on the venue Decreasing the per-diem and just ordering lunch would allow for more variety, but this is a small thing. My attendance in the workshop was personally rewarding. I wished I was able to stay for a long ...

Thank you for completing this survey

Page 12 of 13 Connections for Women: Inverse Problems and Applications, August 19, 2010 to August 20, 2010 at MSRI, Berkeley

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. An (approximate) schedule for the workshop should have been prepared earlier, so one could arrange travelling accordingly. I had to miss a couple of talks because it was not clear at what time the w ...

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Introductory Workshop: Inverse Problems and Applications August 23 to August 27, 2010 MSRI, Berkeley, CA, USA

Organizers: Margaret Cheney (Rensselaer Polytechnic Institute) Gunther Uhlmann* (University of Washington) Michael Vogelius( Rutgers) Maciej Zworski (University of California, Berkeley)

Parent Program: Inverse Problems and Applications

Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Report Introductory Workshop, August 23-27, 2010

Organizing Committee: Margaret Cheney (RPI) Gunther Uhlmann, chair (U. Washington and UC Irvine) Michael Vogelius (Rutgers) Maciej Zworski (UC Berkeley)

Inverse Problems are those where causes for an observed effect are to be determined. In other words, from external observations of a hidden, black box system (patient’s body, nontransparent industrial object, Earth interior, etc.) one needs to recover the unknown parameters of the system. Such problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a vast variety of of medical as well as other (geophysical, industrial, radar, sonar) imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the earths interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modeling in the life sciences. The workshop’s goal was to introduce the participants of the semester long MSRI program Inverse Problems and Applications, as well as other interested students and junior and senior researches to the current state of affairs of some major areas of inverse problems. Although the variety of important areas of inverse problems is too broad to be addressed, even marginally, in a single workshop, an attempt was made to have several mini-courses that would, on one hand, provide some techniques that are used in most IP topics, and on the other hand, present some new developments and outstanding challenges. The workshop consisted of six mini-courses:

• Imaging in Random Waveguides (3 lectures) Lecturer: Liliana Borcea (Rice U.) The topic was the problem of imaging sources/scatterers in random (i.e., with large wave speed fluctuations) waveguides, using measurements of the acoustic pressure field recorded at a remote array of sensors, over some time window. The problems of imaging in random media have been addressed very actively in the recent several years, and the lectures addressed a new direction in this area, which uses the asymptotic theory of wave propagation in such waveguides developed by W. Kohler, G. Papanicolaou and J. Garnier. It was shown how this leads to a robust imaging in such waveguides. A novel incoherent imaging approach was described, based on a special form of transport equations. Recent results by the lecturer, L. Issa, and C. Tsogka were presented. The imaging in random media, albeit being more and more popular lately, is still not known sufficiently well to the inverse problems community, and thus the lectures provided an invaluable introduction to that topic. • Introduction to Radar Imaging (3 lectures) Lecturer: Margaret Cheney (RPI) Radar (and the similar sonar) imaging modality is well known to have numerous civilian and military applications. In this series of lectures, the main mathematical techniques arising in radar imaging were presented, including in particular the ones from scattering theory, PDEs, microlocal analysis, and integral geometry. A large number of practically important issues were listed that are still unresolved and demand mathematical analysis. One of them, for instance,

Page 2 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

is addressing the non-flat, 3D structure of the Earth surface when surveyed by radar equipped airplanes. Close connections to the topics and techniques addressed in other mini-courses were noticed by the lecturer and participants. • An Introduction to Magnetic Resonance Imaging (3 lectures) Lecturer: Charles Epstein (U. Pennsylvania) Magnetic resonance imaging is well known to be one of the major medical diagnostic and biomedical research tools. The functional MRI has already lead to many exciting discoveries. MRI is also a very common modality in chemistry studies and other areas. As in other tomographic techniques, mathematics plays a major role in MRI. The course covered the basic concepts of spin-physics needed to understand the signal equation, and sources of contrast in magnetic resonance imaging, as well as the concepts needed to understand sampling, image reconstruction, the process of selective excitation, and some of the more sophisticated applications of MRI. • Hybrid Methods of Medical Imaging (4 lectures) Lecturer: Peter Kuchment (Texas A&M Traditional tomographic methods employ the same physical kind of radiation both for pene- trating the target and for measuring the response (e.g., X-rays in the standard CT, ultrasound in ultrasound tomography, etc.). Each of these kinds of waves has its advantages and faults, e.g., one of them can provide high contrast and low resolution, while another would do just the opposite. To address these issues (as well as cost, safety, and some other parameters), a variety of new hybrid methods is being currently developed, which involve different types of waves. The purpose is to combine the advantages of each type, while alleviating their individual deficiencies. These new modalities, overwied in the lectures, require new mathematical techniques . The course concentrated on the mathematical problems, results, and challenges of the hybrid modalities (thermo/photo-acoustic and acousto-electric imaging, as well as some others). • 30 Years of Calderón’sProblem (4 lectures) Lecturer: Gunther Uhlmann (UC Irvine and U. Washington) In 1980 Calderónpublished a short paper, in which he pioneered the mathematical study of the inverse problem of determining the conductivity of a medium by making voltage and current measurements at the boundary. This inverse method is also called Electrical Impedance Tomography. There has been fundamental progress made on this problem, which is now called Calderons problem, during the following thirty years, but several fundamental questions remain unanswered. This is still an extremely active area of research. The lectures addressed the most important development – applications of complex geometrical optics. In the last lecture, counterexamples to uniqueness in Calderons problem were discussed. Studying those, the lecturer and his co-authors were led (3 years before the same result obtained by physicists) to discovery of what is now called cloaking and invisibility. The main ideas, recent results, limitations, and possible applications of the cloaking were presented. • Electromagnetic Imaging and the Effect of Small Inhomogeneities (3 lectures) Lecturer: Michael Vogelius (Rutgers U.) A survey of work related to electromagnetic imaging was presented that spans a 20 year period. First, various representation formulas for the perturbations in the electromagnetic fields caused

Page 3 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

by volumetrically small sets of inhomogeneities were considered. The imperfections studied range from a finite number of well separated objects of known (rescaled) shape and of fixed location, to sets of inhomogeneities of quite random geometry and location. It was shown how one can use these representations to design very effective numerical reconstruction algorithms. In the second part of the lectures, the relation between small inhomogeneities and approximate invisibility was discussed. E.g., precise estimates for the degree of approximate invisibility were given. The recent approximate invisibility estimates that are also explicit (and sharp) in their dependence on frequency were also introduced.

All the mini-courses were enthusiastically attended by the participants and drew many questions and discussions during and between the lectures. Although the topics were diﬀerent, it was evident that close ideological and technical relations between these ﬁelds (sometimes maybe even not realized by their practitioners) exist. These links were actively discussed during and after the workshop and will most probably lead to new developments. Graduate students, postdocs, and researchers were presented a wide panorama of inverse problems topics, mathematical techniques, applications, and outstanding challenges.

Page 4 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Invited Speakers firstname lastname institutionname Liliana Borcea Rice University Margaret Cheney Rensselaer Polytechnic Institute Charles Epstein University of Pennsylvania Peter Kuchment Texas A & M University Gunther Uhlmann University of Washington Michael Vogelius Rutgers, The State University of New Jersey

Page 5 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Schedule

Monday, August 23

09:15AM - 09:30AM Introduction 09:30AM - 10:30AM Gunther Uhlmann 30 Years of Calderón's Problem I 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Margaret Cheney Introduction to Radar Imaging I 12:00PM - 02:00PM Lunch An Introduction to Magnetic Resonance Imaging I 02:00PM - 03:00PM Charles Epstein

03:00PM - 03:30PM Tea 03:30PM - 04:30PM Peter Kuchment Hybrid Methods of Medical Imaging

Tuesday, August 24

09:30AM - 10:30AM Peter Kuchment Hybrid Methods of Medical Imaging II 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Charles Epstein An Introduction to Magnetic Resonance Imaging II 12:00PM - 02:00PM Lunch 02:00PM - 03:00PM Margaret Cheney Introduction to Radar Imaging II 03:00PM - 03:30PM Tea 03:30PM - 04:30PM Gunther Uhlmann 30 Years of Calderón's Problem II 04:30PM - 06:00PM Reception

Page 6 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Wednesday, August 25

09:30AM - 10:30AM Margaret Cheney Introduction to Radar Imaging III 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Liliana Borcea Imaging in Random Waveguides I 12:00PM - 02:00PM Lunch Electromagnetic Imaging and the Effect of Small 02:00PM - 03:00PM Michael Vogelius Inhomogeneities I 03:00PM - 03:30PM Tea An Introduction to Magnetic Resonance Imaging 03:30PM - 04:30PM Charles Epstein III

Thursday, August 26

Electromagnetic Imaging and the Effect of Small 09:30AM - 10:30AM Michael Vogelius Inhomogeneities II 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Liliana Borcea Imaging in Random Waveguides II 12:00PM - 02:00PM Lunch 02:00PM - 03:00PM Peter Kuchment Hybrid Methods of Medical Imaging III 03:00PM - 03:30PM Tea 03:30PM - 04:30PM Gunther Uhlmann 30 Years of Calderón's Problem III

Friday, August 27

09:30AM - 10:30AM Liliana Borcea Imaging in Random Waveguides III 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Peter Kuchment Hybrid Methods of Medical Imaging IV 12:00PM - 02:00PM Lunch 02:00PM - 03:00PM Gunther Uhlmann 30 Years of Calderón's Problem IV 03:00PM - 03:30PM Tea Electromagnetic Imaging and the Effect of Small 03:30PM - 04:30PM Michael Vogelius Inhomogeneities III

Page 7 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Officially Registered Participants firstname lastname institutionname Tuncay Aktosun University of Texas Ricardo Alonso Rice University Jennifer Anderson University of Texas Simon Arridge University College London Guillaume Bal Columbia University Elena Beretta Universita' La Sapienza Eric Bonnetier Université de Grenoble I (Joseph Fourier) Liliana Borcea Rice University Fioralba Cakoni Tirana University Thomas Callaghan Stanford University Richard Champion US Geological Survey Lung-Hui Chen National Chung Cheng University Jie Chen University of Washington Margaret Cheney Rensselaer Polytechnic Institute Daeshik Choi University of Washington Francis Chung University of Chicago David Colton University of Delaware Ryan Croke Colorado State University Chris Croke University of Pennsylvania David Dos Santos Ferreira Université de Paris 13 (Nord) Semyon Dyatlov University of California Charles Epstein University of Pennsylvania Malena Espanol Caltech Thomas Fogwell Emory University Brittany Froese Simon Fraser University Ricardo Gallardo Rice University Elizabeth Garcilazo Botello National Autonomous University of Mexico (UNAM) Dmitry Glotov Auburn University Rim GOUIA University of Texas Fernando Guevara Vasquez University of Utah Sarah Hamilton Colorado State University Pilar Herreros Universität Münster Hamid Hezari Massachusetts Institute of Technology Kyle Hickmann Oregon State University Nguyen Hoang Kansas State University Darren Homrighausen Statistics Department Mark Hubenthal University of Washington Seick Kim Yonsei University Dojin Kim Oregon State University ilker kocyigit University of Washington Robert Korsan Decisions, Decisions! Peter Kuchment Texas A & M University Ru-Yu Lai University of Washington Claudia Lara Herrera University of Sao Paulo (USP) Matti Lassas University of Helsinki Kody Law University of Warwick Shitao Liu University of Virginia

Page 8 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Yang Liu University of Pennsylvania Alison Malcolm MIT Alexander Mamonov Rice University Anna Mazzucato Penn State Joyce McLaughlin Rensselaer Polytechnic Institute Robert McOwen Northeastern University Graeme Milton University of Utah Carlos Montalto Purdue University Miguel Montoya Vallejo University of São Paulo (USP) Jose Morales Barcenas Center of Investigations in Mathematics (CIMAT) Shari Moskow Drexel University Alexey Nazarov Novosibirsk State University Tu Nguyen University of Washington Linh Nguyen Texas A & M University Ozan Öktem Royal Institute of Technology (KTH) Lee Patrolia University of Washington Juha-Matti Perkkio Helsinki University of Technology Valter Pohjola University of Helsinki Hai-Hua Qin University of Delaware Lingyun Qiu Purdue University Shelley Rohde University of California, Merced Brigitte Servatius Worcester Polytechnic Institute Jaemin Shin University of Minnesota Twin Cities Samuli Siltanen University of Helsinki Suresh Srinivasamurthy Kansas State University Plamen Stefanov Purdue University Andrew Stuart University of Warwick Ashley Thomas Rensselaer Polytechnic Institute Justin Tittelfitz University of Washington Nilifer Topsakal University of Texas, Arlington Chrysoula Tsogka University of Crete Gunther Uhlmann University of Washington Gerardo Daniel Valencia Martinez National Autonomous University of Mexico (UNAM) András Vasy Stanford University Vianey Villamizar Brigham Young University Michael Vogelius Rutgers, The State University of New Jersey Ryan Walker Department of Mathematics Xiaoming Wang Florida State University Jue Wang Union College--Union University Yan Wang University of Pennsylvania Patcharee Wongsason Oregon State University Ganquan Xie GL Geophysical Lab. Yang Yang University of Washington Yi Zeng University of Illinois at Urbana-Champaign Ting Zhou Unversity of Washington Miren Zubeldia Universidad del País Vasco/Euskal Herriko Unibertsitatea

Page 9 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Officially Registered Participant Information Participants 93

Gender 93 Male 50.54% 47 Female 45.16% 42 Declined to state 4.30% 4

Ethnicity* 96 White 52.08% 50 Asian 23.96% 23 Hispanic 14.58% 14 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 9.38% 9 * ethnicity specifications are not exclusive

Page 10 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

responses

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Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 40 87% partially 6 13% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 32 70% Satisfactory 14 30% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 12 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Above satisfactory 26 57% Satisfactory 20 43% Not satisfactory 0 0% no opinion 0 0%

Additional comments on the topic presentation and organization some of the speakers went through what I thought was too much technical detail rather than focusing on the main ideas MSRI Director and Coordinate Have great effort for INVERSE PROBLEM WORKSHOP, INVE ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 34 74% partially 12 26% no 0 0%

Did the workshop increase your interest in the subject? yes 40 87% partially 6 13% no 0 0%

Page 13 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Was the workshop worth your time and effort? yes 43 93% partially 3 7% no 0 0%

Additional comments on your personal assessment I have created Global and Local Inversion and modeling for Physical, mathematical and Chemical and Biological Problems, GLLH cloak overcome difficulties for invisible cloak materials The workshop was ...

Venue

Your overall experience at MSRI 1 - Above satisfactory 32 70% 2 9 20% 3 3 7% 4 2 4% 5 - Not satisfactory 0 0%

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The assistance provided by MSRI staff 1 - Above satisfactory 30 65% 2 12 26% 3 2 4% 4 2 4% 5 - Not satisfactory 0 0%

Page 14 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

Above satisfactoryNot satisfactory

The physical surroundings 1 - Above satisfactory 34 74% 2 7 15% 3 2 4% 4 2 4% 5 - Not satisfactory 1 2%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 - Above satisfactory 15 33% 2 14 30% 3 11 24% 4 5 11% 5 - Not satisfactory 1 2%

Above satisfactoryNot satisfactory

Additional comments on the venue It doesn't seem to be possible to get the lecture room dark enough to see images projected on the screen. It would be nice to have less sweet stuff and more of the healthful fare. Mathematical Ph ...

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We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. As a long-term visitor, it's hard to get settled (find grocery stores, figure out how to do laundry, etc) while at the same time attending ther workshop and trying to keep up with the usual stream o ...

Page 15 of 16 Introductory Workshop on Inverse Problems and Applications, August 23, 2010 to August 27, 2010 at MSRI, Berkeley

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Page 16 of 16

Inverse Problems: Theory and Applications November 8, 2010 to November 12, 2010 MSRI, Berkeley, CA, USA

Organizers: Liliana Borcea (Rice University) Carlos Kenig (University of Chicago) Maarten de Hoop (Purdue University) Peter Kuchment (Texas A&M University) Lassi Paivarinta (University of Helsinki) Gunther Uhlmann* (University of Washington) Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

Report on the Inverse Problems and Applications, Nov. 8-12, 2010

Organizing Committee: Liliana Borcea (Rice) Maarten de Hoop (Purdue) Carlos Kenig (U. Chicago) Peter Kuchment (Texas A&M Lassi P¨aiv¨arinta (U. Helsinki) Gunther Uhlmann, chair (UC Irvine and U. Washington)

Inverse Problems are those where from “external” observations of a hidden, “black box” system (patient’s body, nontransparent industrial object, Earth’s interior, etc.) one needs to recover the unknown parameters of the system. Such problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a vast variety of of medical as well as other (geophysical, industrial, radar, sonar) imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the earth’s interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modeling in the life sciences. The well attended workshop’s goal was to assemble a large group of senior experts, junior scientists, postdocs and graduate students to assess the current state of research in various sub-fields of the theory and applications of inverse problems. In five days, 21 invited 45-min and 8 invited 30-min lectures were presented, i as well as 15 20-min contributed talks. The 30-min lectures were given by the MSRI postdocs and a visiting graduate student. The talks, which attracted a large audience, gave a spectacular overview of many theoretical and applied contemporary issues of the area. Quite a few presentations were devoted to electromagnetic imaging (such as electrical impedance tomography and its mathematical incarnation - Calderón problem), inverse scattering, and invisibility. In several lectures, close attention was paid to the development of novel imaging methods that carry a high promise for clinical diagnostics, including for instance thermo- and photo-acoustic tomography, acousto-electric tomography, multi-spectral electrical impedance imaging, bio-mechanical imaging, and new generations of ultrasound and optical imaging. Spectral inverse problems were addressed in a several lectures, as well as geophysical imaging, imaging in random media, inverse problems of geometry, PDEs and relativity theory, numerical analysis issues of inverse problems. Radar theory and robust principal component analysis can also be added to this impressive list. Everyone present at the workshop saw a seamless scientific field with numerous flourishing connections between the very diverse areas. This was also evidenced by extremely active discussions during, between, and after talks. It is clear that the communications during the workshop will lead to advances in many of the topics discussed. It is hard to predict the future, especially future research results, but one can envision, for instance, that the methods of robust principal component analysis presented in the wonderful lecture by E. Candes to be applied to treating motion artifacts in radar studies. The geophysical techniques of plane wave stacking are being applied to improve ultrasound medical imaging. Methods developed in integral geometry of thermoacoustic imaging might be helpful in resolving some issues of radar theory, a rich field, not over-populated by mathematicians. The variety of mathematical tools involved was astounding: PDEs, integral and differential geometry, complex analysis, microlocal analysis, optimization, spectral theory, graph theory, probability and statistics etc. The audience contained, besides representatives of academia, also researchers from industry and research labs. These came from many countries from all over the world.

Page 2 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

It is our belief that the workshop will facilitate (and has already started doing so) new developments, collaborations, and results in the vast area of inverse problems and applications.

Page 3 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Simon Arridge University College London Kari Astala University of Helsinki Sergei Avdonin University of Alaska Guillaume Bal Columbia University Assia Benabdallah Centre de mathématiques et informatique Elena Beretta Universita' La Sapienza Eric Bonnetier Université de Grenoble Liliana Borcea Rice University Fioralba Cakoni University of Delaware Emmanuel Candes California Institute of Technology Margaret Cheney Rensselaer Polytechnic Institute Kiril Datchev Massachusetts Institute of Technology Gregory Eskin University of California, Berkeley Dmitry Glotov Auburn University Fernando Guevara Vasquez University of Utah Cristian Gutierrez Temple University Pilar Herreros Universität Münster Hamid Hezari Massachusetts Institute of Technology Isozaki Hiroshi University of Tsukuba David Isaacson Rensselaer Polytechnic Institute Hyeonbae Kang Inha University Philipp Kuegler University of Linz Matti Lassas Helsinki Xiaosheng Li Florida International University Peter Maass University of Bremen FB 03 Alexander Mamonov Rice University Joyce McLaughlin Rensselaer Polytechnic Institute Adrian Nachman University of Toronto Frank Natterer Westfälische Wilhelms-Universität Münster Linh Nguyen Texas A & M University George Papanicolaou Stanford University Pedro Pérez Caro Autonomous University of Madrid Rakesh University of Delaware Kui Ren University of Texas Barbara Romanowicz University of California, Berkeley Mikko Salo University of Helsinki Hart Smith University of Washington Plamen Stefanov Purdue University Faouzi Triki Université de Grenoble I (Joseph Fourier) Leo Tzou University of Helsinki Andras Vasy Stanford University Steven Zelditch Johns Hopkins University Hong-Kai Zhao University of California, Berkeley Ting Zhou University of Washington

Page 4 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

Schedule

Monday, November 08, 2010 9:25AM - 9:40AM Simons Auditorium Welcome 9:40AM - 10:25AM Simons Auditorium George Papanicolaou Imaging with intensities only 10:25AM - 10:55AM Tea 10:55AM - 11:40AM Simons Auditorium Guillaume Bal Hybrid Inverse Problems in Optics Generalized Polarization Tensors: 11:40AM - 12:25PM Simons Auditorium Hyeonbae Kang Mathematics and Applications 12:25PM - 2:00PM Lunch Reconstructing Electromagnetic Obstacles 2:00PM - 2:30PM Simons Auditorium Ting Zhou by the Enclosure Method Scattering rigidity for analytic manifolds 2:30PM - 3:00PM Simons Auditorium Pilar Herreros with a magnetic field 3:00PM - 3:30PM Tea UC Berkeley, Evans MSRI-Evans Lecture @ UC Berkeley Evens 4:10PM - 5:00PM Liliana Borcea 10 Hall Tuesday, November 09, 2010 Biomechanical Imaging in Tissue - Using 9:30AM - 10:15AM Simons Auditorium Joyce McLaughlin Frequency Dependent Data 10:15AM - 10:45AM Tea Stability of inverse problems for heat and 10:45AM - 11:30AM Simons Auditorium Matti Lassas wave equations and the collapse of the dimension Consecutive time reversal in wave equation 11:30AM - 12:15PM Simons Auditorium Frank Natterer imaging 12:15PM - 1:45PM Lunch Thermoacoustic and Photoacoustic 1:45PM - 2:30PM Simons Auditorium Plamen Stefanov Tomography with a variable continuous or discontinuous sound speed Spectral and resonant uniqueness of radial 2:30PM - 3:00PM Simons Auditorium Hamid Hezari potentials 3:00PM - 3:30PM Tea The Inverse Calderón's Problem for 3:30PM - 4:00PM Simons Auditorium Leo Tzou Schroedinger Operators on Riemann Surfaces In Silico Manipulation of Qualitative 4:15PM - 4:35PM Baker Board Room Kuegler Biological Behaviour using Sparsity Enforcing Regularization

Page 5 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

A Rarefraction Problem and Monge-Ampere 4:15PM - 4:35PM Simons Auditorium Cristian Gutierrez Equations Uniqueness And Stability For The Inverse 4:35PM - 4:55PM Simons Auditorium Faouzi Triki Conductivity Problem with Internal Data A boundary value transformation for an 4:35PM - 4:55PM Baker Board Room Dmitry Glotov inverse problem arising in magnetometry Boundary Control Approach to Inverse 4:55PM - 5:15PM Baker Board Room Sergei Avdonin Problems on Graphs Regularization with sparsity constraints and 4:55PM - 5:15PM Simons Auditorium Peter Maass impedance tomography 5:15PM - 7:00PM Reception Wednesday, November 10, 2010 Robust principal component analysis and 9:30AM - 10:15AM Simons Auditorium Emmanuel Candes other advances in low-rank matrix modeling some theory and some applications 10:15AM - 10:45AM Tea

10:45AM - 11:30AM Simons Auditorium Steven Zelditch Spectral rigidity of ellipses among C∞ plane domains with the ellipse symmetry Wave propagation on asymptotically De 11:30AM - 12:15PM Simons Auditorium Andras Vasy Sitter and Anti-de Sitter spaces 12:15PM - 1:45PM Lunch A phase space method for traveltime 1:45PM - 2:30PM Simons Auditorium Hong-Kai Zhao tomography Fernando Guevara Uncertainty quantification in resistor 2:30PM - 3:00PM Simons Auditorium Vasquez network inversion 3:00PM - 3:30PM Tea Resistor networks and optimal grids for 3:30PM - 4:00PM Simons Auditorium Alexander Mamonov electrical impedance tomography with partial boundary measurements 4:15PM - 4:35PM Simons Auditorium Isozaki Hiroshi Inverse Scattering from Cusp Restricted Uniqueness and Stability For a 4:35PM - 4:55PM Simons Auditorium Rakesh Formally Determined Hyperbolic Inverse Problem with a point source Quantitative photoacoustic imaging of 4:55PM - 5:15PM Simons Auditorium Kui Ren multiple coefficients with multiwavelength data Thursday, November 11, 2010 Exploring the limits of visibility in 9:30AM - 10:15AM Simons Auditorium Kari Astala Calderon's inverse problem 10:15AM - 10:45AM Tea Page 6 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

Waveform-Diverse Moving-Target Spotlight 10:45AM - 11:30AM Simons Auditorium Margaret Cheney Synthetic-Aperture Radar Reconstruction in the Calderón Problem 11:30AM - 12:15PM Simons Auditorium Adrian Nachman with Partial Data 12:15PM - 1:45PM Lunch Inverse problems for the anisotropic 1:45PM - 2:30PM Simons Auditorium Mikko Salo Maxwell equations Propagation through trapped sets and 2:30PM - 3:00PM Simons Auditorium Kiril Datchev semiclassical resolvent estimates 3:00PM - 3:30PM Tea Some problems of thermoacoustic 3:30PM - 4:00PM Simons Auditorium Linh Nguyen tomography (TAT) 4:15PM - 4:35PM Simons Auditorium Gregory Eskin Inverse hyperbolic problems and black holes Lipschitz stability for the electrical 4:15PM - 4:35PM Baker Board Room Elena Beretta impedance tomography problem: the complex case Inverse problem for a parabolic system with 4:35PM - 4:55PM Simons Auditorium Assia Benabdallah three components by measurements of one component 4:35PM - 4:55PM Baker Board Room Xiaosheng Li Inverse Problems with Partial Data in a Slab A Stability Result For Electric Impedance 4:55PM - 5:15PM Simons Auditorium Eric Bonnetier Tomography by Elastic Perturbation

Stable determination of electromagnetic 4:55PM - 5:15PM Baker Board Room Pedro Pérez Caro coefficients Friday, November 12, 2010 Recent advances in full waveform global 9:30AM - 10:15AM Simons Auditorium Barbara Romanowicz seismic tomography of the earth's mantle 10:15AM - 10:45AM Tea A Model Error Approximation Method for 10:45AM - 11:30AM Simons Auditorium Simon Arridge NonLinear Tomography Problems Transmission Eigenvalues in Inverse 11:30AM - 12:15PM Simons Auditorium Fioralba Cakoni Scattering Theory 12:15PM - 1:45PM Lunch Decoupling of modes for the elastic wave 1:45PM - 2:30PM Simons Auditorium Hart Smith equation in media of limited smoothness Mathematical Problems in the diagnosis and 2:30PM - 3:15PM Simons Auditorium David Isaacson treatment of disease 3:15PM - 3:45PM Tea

Page 7 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Gaik Ambartsoumian University of Texas Simon Arridge University College London Kari Astala University of Helsinki Sergei Avdonin University of Alaska Guillaume Bal Columbia University Dean Baskin Northwestern University Zakaria Belhachmi Université de Haute-Alsace Assia Benabdallah Centre de mathématiques et informatique Elena Beretta Universita' La Sapienza Eemeli Blåsten University of Helsinki Jan Boman Stockholm University Eric Bonnetier Université de Grenoble Liliana Borcea Rice University Russell Brown University of Ketucky Fioralba Cakoni University of Delaware Thomas Callaghan Rice University Emmanuel Candes California Institute of Technology Thomas Cecil Luminescent Technologies Jie Chen University of Washington Margaret Cheney Rensselaer Polytechnic Institute Daeshik Choi University of Washington Matias Courdurier Universidad de Chile Chris Croke University of Pennsylvania Kiril Datchev Massachusetts Institute of Technology Maarten de Hoop Purdue University Semyon Dyatlov University of California, Berkeley Gregory Eskin University of California, Berkeley Suresh Eswarathasan University of Rochester Raluca Felea Rochester Institute of Technology David Finch Oregon State University Thomas Fogwell Texas A&M University Ricardo Gallardo Rice University Elizabeth Garcilazo Botello National Autonomous University of Mexico (UNAM) Dmitry Glotov Auburn University Allan Greenleaf University of Rochester F. Alberto Grunbaum University of California, Berkeley Fernando Guevara Vasquez University of Utah Cristian Gutierrez Temple University Sarah Hamilton Colorado State University Pilar Herreros Universität Münster Hamid Hezari Massachusetts Institute of Technology Isozaki Hiroshi University of Tsukuba Sean Holman Purdue University

Page 8 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

First Name Last Name Current Institution Yulia Hristova Institute for Mathematics and its Applications Mark Hubenthal University of Washington David Isaacson Rensselaer Polytechnic Institute Hyeonbae Kang Inha University Mirza Karamehmedovic Universität Bremen Carlos Kenig University of Chicago Taufiquar Khan Clemson University Arnold Kim North Carolina State University Seick Kim Yonsei University ilker kocyigit University of Washington Robert Korsan n/a Peter Kuchment Texas A & M University Philipp Kuegler University of Linz Leonid Kunyansky University of Arizona Claudia Lara Herrera Universityp, of São Paulo (USP) y Matti Lassas Helsinki Ossi Lehtikangas University of Eastern Finland Qin Li Florida State University Xiaosheng Li Florida International University Wenjing Liao University of California, Berkeley Shitao Liu University of Virginia Peter Maass University of Bremen FB 03 Alexander Mamonov Rice University Anna Mazzucato Pennsylvania State University Joyce McLaughlin Rensselaer Polytechnic Institute Robert McOwen Northeastern University Fatemeh Mohammadi Ferdowsi University of Mashhad Miguel Montoya Vallejo University of São Paulo (USP) Adrian Nachman University of Toronto Frank Natterer Westfälische Wilhelms-Universität Münster Linh Nguyen Texas A & M University Tu Nguyen University of Washington Esa Niemi University of Helsinki Lauri Oksanen University of Helsinki George Papanicolaou Stanford University Lee Patrolia University of Washington Pedro Pérez Caro Autonomous University of Madrid Juha-Matti Perkkio Helsinki University of Technology Randy Qian Purdue University Lingyun Qiu Purdue University Eric Quinto Tufts University Rakesh University of Delaware Kui Ren University of Texas Luca Rondi Università di Trieste

Page 9 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

First Name Last Name Current Institution Ilan Roth University of California, Berkeley Yanir Rubinstein Stanford University Paul Sacks Iowa State University Barbara Romanowicz University of California, Berkeley Valeriy Serov University of Oulu Jaemin Shin University of Minnesota Twin Cities Samuli Siltanen University of Helsinki Therese Sjödén Linnaeus University, Mikko Salo University of Helsinki Hart Smith University of Washington Ashley Thomas Rensselaer Polytechnic Institute Justin Tittelfitz University of Washington Plamen Stefanov Purdue University HSIAO-CHIEH TSENG University of California, Berkeley Faouzi Triki Université de Grenoble I (Joseph Fourier) Gunther Uhlmann University of Washington Leo tzou University of Helsinki Esa Vesalainen University of Helsinki Shen Wang Purdue University Herwig Wendt Purdue University Ganquan Xie GL Geophysical Lab YANG YANG University of Washington Evren Yarman Schlumberger - WesternGeco David Yuen Lake Forest College Andras Vasy Stanford University Anna Zemlyanova Texas A & M University Steven Zelditch Johns Hopkins University Hong-Kai Zhao University of California, Berkeley Miren Zubeldia Universidad del País Vasco/Euskal Herriko Unibertsitatea Ting Zhou University of Washington

Page 10 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 117

Gender 117 Male 70.09% 82 Female 17.95% 21 Declined to state 11.97% 14

Ethnicity* 117 White 50.43% 59 Asian 20.51% 24 Hispanic 8.55% 10 Pacific Islander 0.85% 1 Black 0.00% 0 Native American 0.00% 0 Declined to state 19.66% 23 * ethnicity specifications are not exclusive

Page 11 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 43 91% partially 4 9% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 33 70% Satisfactory 12 26% Not satisfactory 1 2% no opinion 1 2%

Was there adequate time between lectures for discussion?

Page 13 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA Above satisfactory 10 21% Satisfactory 29 62% Not satisfactory 7 15% no opinion 1 2%

Additional comments on the topic presentation and organization schedule was very packed i WAS DEEPLY DISAPPOINTED BY THE DIVISION OF THE TALKS ON PARALLEL SECTIONS.tHE RESULT WAS THAT ON PARALLEL SECTIONS NO VIDEO WAS TAKEN AND THERE WAS NONOTETAKER..i THINK TH ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 38 81% partially 9 19% no 0 0%

Did the workshop increase your interest in the subject?

Page 14 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA yes 36 77% partially 10 21% no 1 2%

Was the workshop worth your time and effort? yes 41 87% partially 6 13% no 0 0%

Additional comments on your personal assessment It was excellent! I think that the existence of parallel sessions for contributed talks created the second rate talks. The problem is not the length of the talks, but the absence of videotaping and n ...

Venue

Your overall experience at MSRI 1 - Above satisfactory 30 64% 2 14 30% 3 1 2% 4 1 2% 5 - Not satisfactory 1 2%

Above satisfactoryNot satisfactory

Page 15 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA The assistance provided by MSRI staff 1 - Above satisfactory 32 68% 2 11 23% 3 2 4% 4 2 4% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The physical surroundings 1 - Above satisfactory 33 70% 2 10 21% 3 2 4% 4 2 4% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 - Above satisfactory 4 9% 2 14 30% 3 17 36% 4 8 17% 5 - Not satisfactory 4 9%

Above satisfactoryNot satisfactory

Additional comments on the venue Lunch could have been better. Coffee breaks were excellent. Video in Simons Aud. needs to be improved! A number of speakers from having interesting slides become illegible when projected. For workshop ...

Page 16 of 17 Inverse Problems: Theory and Applications, November 8, 2010 to November 12, 2010 at MSRI, Berkeley, CA, USA Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. There should be the option to leave questions blank. Overall, this was a wonderful workshop. No real suggestions for improvement. This was a great workshop. Get blackout shades for all the windows in ...

Number of daily responses

Page 17 of 17

Connections for Women: Free Boundary Problems, Theory and Applications January 13, 2011 to January 14, 2011 MSRI, Berkeley, CA, USA

Organizers: Catherine Bandle (University of Basel) Claudia Lederman (University of Buenos Aires) Noemi Wolanski (University of Buenos Aires) Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Report

General remarks

Summary of the talks

Page 2 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Conclusions

Page 3 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Darya Apushkinskaya Universität des Saarlandes Myoungjean Bae Northwestern University Catherine Bandle Universität Basel Lorena Bociu University of Virginia Donatella Danielli Purdue University Maria del Mar Gonzalez Technical University of Catalonia Vera Mikyoung Hur University of Illinois at Urbana-Champaign Benedetta Noris Università di Milano - Bicocca Mariel Saez Trumper P. Universidad Catolica de Chile Susanna Terracini Università di Milano - Bicocca Nina Uraltseva Steklov Mathematical Institute, St. Petersburg Noemi Wolanski Ciudad Universitaria. Pabellon I

Page 4 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Schedule Thursday, January 13, 2011 8:55AM - 9:10AM Simons Auditorium Welcome 9:10AM - 10:00AM Simons Auditorium Catherine Bandle Optimization Problems for Domain Functionals 10:00AM - 11:00AM Tea A Brief Overview on the Parabolic 11:00AM - 11:30AM Simons Auditorium Darya Apushkinskaya Obstacle-type Problem Uniqueness and Stability of Solitary Water 11:40AM - 12:10PM Simons Auditorium Vera Mikyoung Hur Waves 12:10PM - 2:10PM Lunch 2:10PM - 3:00PM Simons Auditorium Susanna Terracini On some Optimal Partition Problems 3:00PM - 3:50PM Tea Multiple-layer Solutions to the Allen-Cahn 3:50PM - 4:20PM Simons Auditorium Mariel Saez Trumper Equation on Hyperbolic Space Existence for a Linearized Steady-State Fluid- 4:30PM - 5:00PM Simons Auditorium Lorena Bociu Nonlinear Elasticity Interaction Friday, January 14, 2011 9:00AM - 9:50AM Simons Auditorium Noemi Wolanski Bernoulli Type Free Boundary Problems 10:00AM - 10:30AM Simons Auditorium Myoungjean Bae Transonic Shocks and Free Boundary Problems 10:30AM - 11:00AM Tea Optimal Regularity and the Free Boundary in 11:00AM - 11:30AM Simons Auditorium Donatella Danielli The Parabolic Signorini Problem A Free Boundary Problem Arising in the 11:40AM - 12:10PM Simons Auditorium Benedetta Noris Context of Bose-Einstein Condensation 12:10PM - 2:10PM Lunch 2:10PM - 3:00PM Simons Auditorium Nina Uraltseva Two Phase Free Boundary Problems Maria del Mar 3:05PM - 3:35PM Simons Auditorium A Free Boundary Model for Price Formation Gonzalez 3:35PM - 4:00PM Tea 4:00PM - 5:00PM Commons 2nd floor Panel Discussion

Page 5 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Darya Apushkinskaya Universität des Saarlandes Myoungjean Bae Northwestern University Catherine Bandle Universität Basel Lorena Bociu University of Virginia Dorin Bucur Université de Savoie (Chambéry) Donatella Danielli Purdue University Maria del Mar Gonzalez Technical University of Catalonia Guanghao Hong Xi'an Jiaotong University Vera Mikyoung Hur University of Illinois at Urbana-Champaign Mihaela Ifrim University of California, Berkeley Sunnie Joshi Texas A & M University Lami Kim Seoul National University Claudia Lederman University of Buenos Aires Hiroyoshi Mitake University of California, Berkeley Fatemeh Mohammadi Ferdowsi University of Mashhad Benedetta Noris Università di Milano - Bicocca Betul Orcan University of Texas Veronica Quitalo University of Texas Mariel Saez Trumper P. Universidad Catolica de Chile Leili Shahriyari Johns Hopkins University Wenhui Shi Purdue University Susanna Terracini Università di Milano - Bicocca Nilifer Topsakal University of Texas, Arlington Hung Tran University of California, Berkeley Ko Woon Um University of Iowa Mehmet Unlu University of Texas Nina Uraltseva Steklov Mathematical Institute, St. Petersburg Monica Visan University of California, Berkeley Zhen Wei University of Virginia Noemi Wolanski Ciudad Universitaria. Pabellon I

Page 6 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 30

Gender 30 Male 16.67% 5 Female 83.33% 25 Declined to state 0.00% 0

Ethnicity* 30 White 46.67% 14 Asian 36.67% 11 Hispanic 3.33% 1 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 13.33% 4 * ethnicity specifications are not exclusive

Page 7 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 14 100% partially 0 0% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 12 86% Satisfactory 2 14% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 9 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

Above satisfactory 10 71% Satisfactory 4 29% Not satisfactory 0 0% no opinion 0 0%

Additional comments on the topic presentation and organization Top quality seminars everything went perfect from my point of view It was very informative and friendly workshop for me:)

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 13 93% partially 1 7% no 0 0%

Did the workshop increase your interest in the subject?

Page 10 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

yes 11 79% partially 3 21% no 0 0%

Was the workshop worth your time and effort? yes 14 100% partially 0 0% no 0 0%

Additional comments on your personal assessment I ahve learned a lot organizing this workshop was certainly worth my time and effort

Venue

Your overall experience at MSRI

Page 11 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

1 - Above satisfactory 11 79% 2 2 14% 3 0 0% 4 1 7% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff 1 -Above satisfactory 9 64% 2 3 21% 3 1 7% 4 0 0% 5 -Not satisfactory 1 7%

Above satisfactoryNot satisfactory

The physical surroundings 1 -Above satisfactory 12 86% 2 1 7% 3 0 0% 4 1 7% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Page 12 of 13 Connections for Women: Free Boundary Problems, Theory and Applications, January 13 to 14, 2011 at MSRI, Berkeley, CA, USA

The food provided during the workshop 1 -Above satisfactory 2 14% 2 5 36% 3 7 50% 4 0 0% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Additional comments on the venue Being at MSRI was a wonderful experience. I wish I could stay longer! The help in terms of organization of the workshop was not satisfactory. In particular, the information on what was expected from ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. As an organizer I think that it could be better if participants received the answer to their request for support a little bit in advance I appreciated in the particular the connections for women

Number of daily responses

Page 13 of 13

Introductory Workshop: Free Boundary Problems, Theory and Applications January 18, 2011 to January 21, 2011 MSRI, Berkeley, CA, USA

Organizers: Tatiana Toro* (University of Washington) Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Report on MSRI Introductory Workshop: Free Boundary Problems, Theory and Applications

Organizers: Lawrence C. Evans (UC Berkeley) & Tatiana Toro (University of Washington)

January 18 - 21, 2011

1 General description

Problems in physics, industry, finance and biology can often be described by partial differential equations that exhibit a priori unknown sets, such as interfaces, moving boundaries or shocks for example. The study of such sets, known as free boundaries, plays a central role in the understanding of such problems. The aim of this workshop was to introduce several free boundary problems arising in completely different areas. One of our goals was for the audience to be able to appreciate the wide variety of questions arising in this area. Special emphasis was made both on the similarities and the differences that come up when addressing each problem.

To achieve our goal we opted for a mini-course format. There were four mini-courses that met for an hour a day four days in a row (Tuesday- Friday). The speakers were leaders in their ﬁeld. P. Daskalopoulos discussed free boundary problems arising in geometric analysis. M. Feldmann discussed free boundary problems arising in shock analysis. I. Kim presented problems in which homogenization techniques are applied to understand free boundary problems. A. Petrosyan discussed various monotonicity formulas which play a fundamental role in understanding the regularity of the free boundary in several diﬀerent problems. The talks were aimed at the postdocs in the area.

A special effort was made to encourage the women who participated in the Connections for Women workshop which took place January 13-14, 2011 to stay over the weekend and participate in the introductory workshop. In fact we extended invitations to some women who had applied for the first but not for the second workshop. We were successful and our audience was over 35% female. One of our main guidelines in making funding decisions was to offer support to participants in earlier stages of their careers with little access to personal or institutional grants. We encouraged more senior participants to use such grants to cover their expenses whenever possible. As a consequence junior mathematicians constituted the largest percentage of the audience.

Page 2 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

2 Highlights of the mini-courses

We brieﬂy describe the content of each one of the mini-courses.

2.1 Degenerate Geometric Flows and related Free-Boundary Problems - P. Daskalopoulos

n+1 In this course she discussed the evolution of hypersurfaces in R by functions of their principal curvatures. The examples included the evolution by powers of the Gaussian curvature and the Harmonic mean curvature flow. Such flows lead to fully-nonlinear parabolic partial differential equations which become degenerate at points or interfaces where one or more of the principal curvatures vanish. She emphasized that the question of the optimal regularity of solutions is often connected to the study of the related free-boundary problem.

The topics presented included:

• An overview of the geometric ﬂows arising by the evolution of hypersurfaces by functions of their principal curvatures.

• Short time existence of solutions with optimal regularity and related degenerate linear problems. Sharp a priori estimates. Special attention was given to the change of variable techniques which determine the function space where one can expect regularity. This apparently purely technical point has been one of her crucial contributions to the area.

• Long time existence of regular solutions.

• Development of singularities.

• Open problems

2.2 Free Boundary Problems in Shock Analysis - M. Feldmann

Shock waves, which arise in physical situations involving gases or compressible fluids, often exhibit complex structures which are not well understood. This phenomena was first described by Ernst Mach in 1878. He described the sound effects observed during the supersonic motion of a projectile. He deduced and experimentally confirmed the existence of a shock wave which has the form of a cone with the projectile at the apex. Since then experimental and computational studies as well as asymptotic analysis have shown that various patterns of reflected shock waves may occur. However, many fundamental issues related to shock reflection are not yet understood, including the transition between different reflection patterns. In recent work M. Feldmann has contributed to establish the mathematical theory of shock reflection. To some extent the goal of the course was to give an overview of the area and describe the state of the art.

Page 3 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

The topics presented included:

• Basic equations of gas dynamics: steady and self-similar compressible Euler system and potential ﬂow equation. These equations are of mixed elliptic-hyperbolic type. The shocks correspond to certain discontinuities in the solutions. In many cases, the study of solutions with shocks can be reduced to solving a free boundary problem for the elliptic part of the solution.

• Discussion of the existence, stability and regularity of steady and self-similar solutions with shocks. Especial attention was given to the shock reﬂection problem.

2.3 Homogenization for free boundary problems -I. Kim

The goal of this mini-course was to introduce the audience to the theory of homogenization and its applications to free boundary problems with oscillatory boundary conditions. She presented several examples to convey the idea that homogenization should be understood as an averaging process. She presented the notion of viscosity solution and the corresponding maximum principles. Through examples she introduced several of the techniques which are used in this area to prove that the limiting process associated with the homogenization problem converges.

2.4 Monotonicity formulas and obstacle type problems - A. Petrosyan

The goal of this mini-course was to discuss several types of monotonicity formulas (Alt-Caffarelli- Friedman, Almgren, Weiss, Monneau) and their generalizations to study different aspects of obstacle type problems, such as the optimal regularity, classification of free boundary points, the study of blowups, the regularity of the free boundary, and the structure of the singular set.

On the ﬁrst day he provided notes to the participants which can be found in the MSRI web page. His mini-course was organized as follows:

• Lecture 1: General description of several obstacle type problems and classical W 2,p regularity of the solutions.

• Lecture 2: ACF monotonicity formula. Application: Optimal regularity in obstacle type problems.

• Lecture 3: Weisss type monotonicity formulas as used in the study of the free boundary of obstacle type problems. Application: Study of the homogeneous global solutions obtained as blow-ups and classiﬁcation of free boundary points.

• Lecture 4: Almgrens frequency formula as used in the study of the Signorini Problem. Ap- plication: Study of the homogeneous global solutions obtained as blow-ups.

Page 4 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Panagiota Daskalopoulos Columbia University Mikhail Feldman University of Washington Inwon Kim University of California, Berkeley Arshak Petrosyan Purdue University

Page 5 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Schedule

Tuesday, January 18, 2011

9:25AM - 9:40AM Simons Auditorium Welcome Degenerate Geometric Flows and related 09:40AM - 10:40AM Simons Auditorium Toti Daskalopoulos Free-Boundary Problems 10:40AM - 11:10AM Tea 11:10AM – 12:10PM Simons Auditorium Mikhail Feldmann Free Boundary Problems in Shock Analysis 12:10PM - 2:00PM Lunch Homogenization for free boundary 2:00PM - 3:00PM Simons Auditorium Inwon Kim problems 3:00PM - 3:30PM Tea Monotonicity formulas and obstacle type 3:30PM - 4:30PM Simons Auditorium Arshak Petrosyan problems 4:30PM – 6:00PM Reception

Wednesday, January 19, 2011 to Friday, January 21, 2011

Degenerate Geometric Flows and related 09:30AM - 10:30AM Simons Auditorium Toti Daskalopoulos Free-Boundary Problems 10:30AM - 11:00AM Tea 11:00AM – 12:00PM Simons Auditorium Mikhail Feldmann Free Boundary Problems in Shock Analysis 12:00PM - 2:00PM Lunch 2:00PM - 3:00PM Simons Auditorium Inwon Kim Homogenization for free boundary problems 3:00PM - 3:30PM Tea Monotonicity formulas and obstacle type 3:30PM - 4:30PM Simons Auditorium Arshak Petrosyan problems

Page 6 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Mark Allen Red Rocks Matthew Badger Washington University Myoungjean Bae Northwestern University Dorin Bucur Université de Savoie (Chambéry) Ramon Calderer University of Illinois Vladimir Chernyy University of Oxford Marc Conrad University of Wisconsin Panagiota Daskalopoulos Columbia University Olivaine de Queiroz State University of Campinas (UNICAMP) Fabrice Debbasch Northwestern University Hongjie Dong Brown University SEDA ERMIS n/a Craig Evans University of California, Berkeley Mikhail Feldman University of Washington Maria del Mar Gonzalez University of Texas Viktor Grigoryan University of California, Berkeley Senoussi Guesmia Abdus Salam International Centre for Theoretical Physics Mahir Hadzic Universität Zürich Guanghao Hong Xi'an Jiaotong University Mihaela Ifrim University of California, Davis Sunnie Joshi Texas A & M University Inwon Kim University of California, Berkeley Lami Kim Seoul National University Seick Kim Yonsei University Robert Korsan n/a gualdani Maria University of Texas Henok Mawi Temple University Hiroyoshi Mitake University of California, Berkeley Kaj Nystrom University of Umeå BETUL ORCAN University of Texas Arshak Petrosyan Purdue University Norbert Pozar University of California, Los Angeles Veronica Quitalo University of Texas Dipendra Regmi Oklahoma State University Leili Shahriyari Johns Hopkins University

Page 7 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Wenhui Shi Purdue University Nilifer Topsakal University of Texas, Arlington Tatiana Toro University of Washington MEHMET UNLU University of Texas Noemi Wolanski Depto. de Matematica. FCEN - UBA Ray Yang University of Texas

Page 8 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 41

Gender 41 Male 58.54% 24 Female 39.02% 16 Declined to state 2.44% 1

Ethnicity* 41 White 58.54% 24 Asian 26.83% 11 Hispanic 2.44% 1 Pacific Islander 0.00% 0 Black 2.44% 1 Native American 0.00% 0 Declined to state 9.76% 4 * ethnicity specifications are not exclusive

Page 9 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 27 90% partially 2 7% no 0 0% no opinion 1 3%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 18 60% Satisfactory 11 37% Not satisfactory 0 0% no opinion 1 3%

Was there adequate time between lectures for discussion?

Page 11 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

Above satisfactory 20 67% Satisfactory 9 30% Not satisfactory 1 3% no opinion 0 0%

Additional comments on the topic presentation and organization wonderful program

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 26 87% partially 4 13% no 0 0%

Did the workshop increase your interest in the subject?

Page 12 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

yes 27 90% partially 3 10% no 0 0%

Was the workshop worth your time and effort? yes 26 87% partially 4 13% no 0 0%

Additional comments on your personal assessment

Venue

Your overall experience at MSRI

Page 13 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

1 - Above satisfactory 23 77% 2 7 23% 3 0 0% 4 0 0% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff 1 -Above satisfactory 22 73% 2 7 23% 3 1 3% 4 0 0% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The physical surroundings 1 -Above satisfactory 25 83% 2 5 17% 3 0 0% 4 0 0% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Page 14 of 15 Introductory Workshop: Free Boundary Problems, Theory and Applications, January 18 to 21, 2011 at MSRI, Berkeley, CA, USA

The food provided during the workshop 1 -Above satisfactory 4 13% 2 14 47% 3 10 33% 4 2 7% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Additional comments on the venue The catarer's food was not satisfactory Sorry about my rating of the food, but I missed having something warm for lunch. This is a comment about the survey. In most surveys that I've taken 5 would be ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. Perhaps give each lecturers less presentation time but have more lecturers. This may help provide a more comprehensive overview of what's going on in the field.

Number of daily responses

Page 15 of 15

Free Boundary Problems, Theory and Applications March 7, 2011 to March 11, 2011 MSRI, Berkeley, CA, USA

Organizers: John King (University of Nottingham) Arshak Petrosyan* (Purdue University) Henrik Shahgholian (Royal Institute of Technology) Georg Weiss (University of Dusseldorf)

Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

REPORT ON THE MSRI WORKSHOP FREE BOUNDARY PROBLEMS, THEORY & APPLICATIONS MARCH 7–11, 2011

Organizers John King (University of Nottingham, UK) Arshak Petrosyan (Purdue University, USA) Henrik Shahgholian (Royal Institute of Technology, Sweden), Chairman Georg Weiss (University of Dusseldorf,¨ Germany)

1. OBJECTIVESAND HISTORICAL PERSPECTIVE Free boundary problems (FBPs) are today considered as one of the most important directions in the main- stream of the analysis of partial differential equations (PDEs), with an abundance of applications in various sciences and real world problems. In the last two decades, various new ideas, techniques, and methods have been developed, and new important, challenging problems in physics, industry, finance, biology, and other areas have arisen. One of the earliest manifestations of FBPs as a separate mathematical discipline was the famous event held in Montecantini, Italy, in 1981, which set a pattern of regular meetings of the FBP community under the name of Free Boundary Problems: Theory & Applications, which held every 2-3 years at various location throughout the world. The thematic program at MSRI in Spring 2011 should be considered as a continuation of this tradition (constituting the 12th meeting in the series). The workshop held on March 7–11, 2011, was one of the main highlights of the program. The main purpose of the workshop was to reflect on the recent exciting developments and advancements in FBPs covering a wide spectrum of theoretical and applied topics, including: FBPs for nonlocal integro-differential operators, FBPs in hyperbolic conservation laws, Laplacian growth and Abelian sandpiles, problems governed by Navier-Stokes, p-Laplacian, porous media, and thin-film equations, quadrature domains, modelling problems in biology, elasto-plasticity, and electrowetting, homogenization of FBPs, and computational surface and interface PDEs. The breadth of the subject presents challenges and opportunities and the workshop intended to facilitate the interactions between various branches of FBPs. The speakers included distinguished members of the FBP community such as L. Caffarelli, A. Friedman, and J. Ockendon and the junior speakers such as J. Jang and L. Levine. A large part of the participants were graduate students and post-doctoral fellows, so we have encouraged speakers to include a significant introductory part in the talks and give ample motivations for the problems. In our funding too we gave priority to graduate students and the participants in earlier stages of their carrier with little or no access to individual or institutional grants, while encouraging more senior participants to use such grants for their expenses whenever possible. Overall, we believe that the workshop was very inspirational and stimulating for younger and more experienced FBP researchers alike, and paved the road for more exciting new developments, in the best of the tradition set in Montecantini in 1981. 1

Page 2 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

2 FREE BOUNDARY PROBLEMS

2. SCIENTIFIC DESCRIPTIONAND HIGHLIGHTSOFTHE TALKS Nonlocal equations. One of the most active areas of the theoretical FBPs at the moment are the problems governed by nonlocal integro-differential equations, such as the fractional Laplacian, which arise in a variety of applications from math finance to biology and theory of elasticity. L. Caffarelli, one of our most distinguished speakers, gave a talk on the parabolic free boundary problem for the fractional heat equation which originated in math finance (joint work with A. Figalli). The talk included also an insightful overview of the breakthrough advancement in the stationary version in the problem (the so-called scalar Signorini problem), joint with I. Athanasopoulos, that has ignited the interest in problems with nonlocal operators. The special Evans lecture given by J.-L. Vazquez, which was the integral part of the workshop, was dedicated to the overview of the porous medium equation and its recent new generalizations leading to nonlocal equations. Contact problems. Historically, one of the first free boundary problems considered were the contact problems in elasto-plasticity (Signorini problem, Herz problems). Over the years they led to the development of so-called variational inequalities, that have not only theoretical but also computational significance. J. Ock- endon, a veteran member of the community, gave a nice overview of such problems and described a recent work on an elastoplastic model where the applied stress greatly exceeds the yield stress. In another talk, N. Garofalo reported on the new results for the parabolic Signorini problem (or the parabolic thin obstacle problem) that has extended the known optimal regularity and free boundary regularity results of I. Athanasopoulos and L. Caffarelli. The time independent Signorini problem is closely related to the obstacle problem for the fractional Laplacian and thus also closely related to the talk by L. Caffarelli. In the third talk on contact problems, N. Matevosyan has reported on the on-going project with A. Pet- rosyan on the study of the free boundary in the Signorini problem near the fixed boundary, which corresponds to the study of the contact set of an elastic body at rest on a surface, where the part of the body is “glued” to the surface. Mathematical biology. Recent years saw an increased activity in the rigorous study of the mathematical models in biology, particularly the problems that exhibit free boundaries. A leading figure in this development is A. Friedman, one the most senior and distinguished scientists working in FBPs. In his talk, he gave an overview of the modelling efforts for the wound healing, which lead to a free boundary problem for a complex system of parabolic/hyperbolic equations. It has to be mentioned, that A. Friedman, M. Herrero, and L. Caffarelli are organising a workshop Free Boundary Problems in Biology to be held at the Mathematical Biology Institute, the Ohio State University, in November, 2011, which in a sense is a continuation of our workshop. Modelling and computations. Since many of the free boundary problems arise in real world applications, a significant importance should be given to the computational counterpart of the field. Two talks has been given in that direction. R. Nochetto discussed the results about modelling of the electrowetting on dielectric that has potential applications in biomedical ‘lab-on-a-chip’ devices (e.g. for automated DNA testing). Among other models, he has described a diffuse interface 3d model for incompressible two-phase flows with moving contact lines that can be successfully computed by using a fully discrete scheme based on fractional time stepping. C. Elliott gave an overview of what is called Computational Surface PDEs, the computational methods of solving PDEs on evolving surfaces. Such problems typically arise in the study of biomembranes, pattern formation, and the study of binary allows. p-Laplacian equation. In a series of recent works, J. Lewis and K. Nystrom¨ have achieved a significant progress in the study of one and two-phase problems governed by the p-Laplacian equation, by establishing a highly nontrivial generalization of the boundary Harnack principle. In his talk, K. Nystrom¨ described the

Page 3 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

FREE BOUNDARY PROBLEMS 3 most recent work in this direction concerning the regularity for the p-Laplace operator in Reifenberg flat or Ahlfors regular NTA-domains, generalizing the previous work by C. Kenig and T. Toro for the classical case p 2. = Higher order equations. A. Mellet reported on a progress in the study of the contact line in the thin film equation, which is a forth order degenerate equation arising in the modelling of small viscous droplets on solid supports. Only very limited results on the existence are known (due to F. Otto) when the contact angle is nonzero. A. Mellet described a new approach (regularization) in an attempt to generalize Otto’s work. Laplacian growth. Two talks were dedicated to the fascinating new developments in the Laplacian growth models, in particular the internal DLA, Rotor-Router, and other related models. Y. Peres has talked about the scaling limits in those models and their convergence to well known objects in FBP: the quadrature domains. L. Levine has talked about recent works with D. Jerison and S. Sheffield on the speed of the deviation from the limit shape in the case of the circular limits. Even though a significant progress has been made in these problems in recent years, there is still no complete understanding of the limiting shapes in certain growth models (such as the Abelian sandpiles), posing new challenging problems for future study. Quadrature domains. One of the classical objects in FBPs, the quadrature domains have gained a new momentum recently with the discovery of H. Shahgholian and collaborators of the so-called two-phase quadrature domains, motivated by the problems in potential theory. In his talks, S. Gardiner gave a nice overview of these new objects and reported on a progress in this direction. Conservation laws. The shocks, vortex sheets, and entropy waves (and more general discontinuity sets) in conservation laws is another example of challenging free boundary problems. G.-Q. Chen gave a comprehensive overview of the origins and the state of the arts in many problems governed by hyperbolic conservation laws. Gas and fluid dynamics. Interesting problems in gas and fluids dynamics are to understand the behavior of the aero/hydrodynamical flows near the boundary with a vacuum. The motivation for such problems is the study of gaseous stars in vacuum or the gas flows in porous medium. In her talk, J. Jang reported on a recent progress in the rigorous study of such problems, including the stability theory of Lane-Emden equilibrium stars. Free boundary problems in fluid dynamics also naturally arise in the presence of two fluids. In certain cases this leads to well-known instabilities, such as the Rayleigh-Taylor instability. G. Simonett described a recent work with J. Pruss¨ on the local well-posedness of the problem in the presence of such instability and even the instantaneous real analyticity of the interface between two fluids. Homogenization. An important question that has been raised in recent years is the homogenization limit of free boundaries in a periodic or random medium. This turns out to be highly nontrivial since even the homogenization of the oscillating Dirichlet or Neumann data on a fixed surface depends strongly on the (ir)rationality of the normals to the surface. In his talk, K. Lee discussed recent results in this direction. Unique continuation. One of the most basic questions in the analysis of PDEs is whether the solutions satisfy the unique continuation property. While it is s fairly well understood for linear elliptic equations, very few results are known for the nonlinear equations. L. Silvestre described a recent result in arguably the simplest case in which one cannot linearize the equation apriori, based on a partial regularity result of O. Savin for fully nonlinear elliptic equations. The classical obstacle problem. R. Monneau presented extremely elegant results about pointwise regularity of the free boundary for the obstacle problem. The results are applicable under minimal assumptions on the regularity of the coefficients (Dini). Similar estimates also hold in the parabolic obstacle problem.

Page 4 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Luis Caffarelli University of Texas Gui-Qiang Chen University of Oxford Charles Elliott University of Warwick Avner Friedman Ohio State University Stephen Gardiner University of California, Davis Nicola Garofalo Purdue University Juhi Jang Cournat Institute of Mathematical Sciences Ki-Ahm Lee Seoul National University Lionel Levine Massachusetts Institute of Technology Norayr Matevosyan University of Cambridge Antoine Mellet University of Maryland Regis Monneau University of Marne-la-Vallée Ricardo Nochetto University of Maryland Kaj Nyström University of Umeå John Ockendon University of Oxford Yuval Peres Microsoft Research Ovidiu Savin Columbia University Luis Silvestre University of Chicago Gieri Simonett Vanderbilt University Juan Vazquez Ciudad Univ. de Canto Blanco

Page 5 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

Schedule

Monday, March 07, 2011 Simons 9:00AM - 9:15AM Welcome Auditorium Simons Avner 9:15AM - 10:15AM A Free Boundary Problem Modeling Wound Healing Auditorium Friedman 10:15AM - 11:00AM MSRI Tea Simons 11:00AM - 12:00PM Luis Silvestre On Unique Continuation for Nonlinear Elliptic Equations Auditorium 12:00PM - 2:00PM MSRI Lunch Simons 2:00PM - 3:00PM Yuval Peres Laplacian Growth and the Mystery of the Abelian Sandpile Auditorium 3:00PM - 3:45PM MSRI Tea Nonlinear diffusion and free boundaries. From porous media 4:10PM - 5:00PM UC Berkeley Juan Vazquez to fractional diffusion Tuesday, March 08, 2011 Simons Regularity properties of the non local parabolic obstacle 9:00AM - 10:00AM Luis Caffarelli Auditorium problem 10:00AM - 10:30AM MSRI Tea Simons On the Rayleigh-Taylor Instability for the Two-Phase 10:30AM - 11:30AM Gieri Simonett Auditorium Navier-Stokes Equations Simons 11:30AM - 12:30PM Juhi Jang Vacuum in Gas and Fluid Dynamics Auditorium 12:30PM - 2:00PM MSRI Lunch Simons 2:00PM - 3:00PM Antoine Mellet A Free Boundary Problem for Thin Films Auditorium 3:00PM - 3:30PM MSRI Tea Simons Nicola Optimal regularity and the study of the free boundary in the 3:30PM - 4:30PM Auditorium Garofalo parabolic Signorini problem 5:30PM - 7:30PM UC Berkeley Party at Craig Evans’ Wednesday, March 09, 2011 Simons 9:00AM - 10:00AM Charles Elliott Computational Surface Partial Differential Equations Auditorium 10:00AM - 10:30AM MSRI Tea

Page 6 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

Simons John 10:30AM - 11:30AM Free Boundary Problems in Elastoplasticity Auditorium Ockendon

Simons Regularity and Free Boundary Regularity for the p -Laplace 11:30AM - 12:30PM Kaj Nyström Auditorium Operator in Reifenberg flat and Ahlfors Regular NTA- Domains Thursday, March 10, 2011 Simons Ricardo Electrowetting on Dielectric: Modeling, Analysis and 9:30AM - 10:30AM Auditorium Nochetto Computation 10:30AM - 11:00AM MSRI Tea Simons Boundary Regularity for a Class of Solutions to the 11:00AM - 12:00PM Ovidiu Savin Auditorium Monge-Ampere Eqation 12:00PM - 2:00PM MSRI Lunch Simons Regis 2:00PM - 3:00PM Free Boundary Pointwise Estimates for the Obstacle Problem. Auditorium Monneau 3:00PM - 3:30PM MSRI Tea Simons Stephen 3:30PM - 4:30PM Two-Phase Quadrature Domains Auditorium Gardiner Friday, March 11, 2011 Simons Gui-Qiang 9:30AM - 10:30AM Free Boundary Problems in Conservation Laws Auditorium Chen 10:30AM - 11:00AM MSRI Tea Simons 11:00AM - 12:00PM Lionel Levine Logarithmic Fluctuations from Circularity Auditorium 12:00PM - 2:00PM MSRI Lunch Simons Homogenization of the Oscillating Data on a Lower 2:00PM - 3:00PM Ki-Ahm Lee Auditorium Dimensional Surface 3:00PM - 3:30PM MSRI Tea Simons Norayr 3:30PM - 4:30PM A Boundary Obstacle Problem Near Fixed Boundary Auditorium Matevosyan

Page 7 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Mark Allen Red Rocks John Andersson University of Warwick Daria Apushkinskaya Universität des Saarlandes Hantaek Bae University of Maryland Emmanuel Bakare Lead City University Mahmoudreza Bazarganzadeh Stockholm University Dorin Bucur Université de Savoie (Chambéry) Luis Caffarelli University of Texas Gui-Qiang Chen University of Oxford Marc Conrad University of Wisconsin Olivaine de Queiroz State University of Campinas (UNICAMP) Charles Elliott University of Warwick Craig Evans University of California, Berkeley Mikhail Feldman University of Wisconsin Avner Friedman Ohio State University Stephen Gardiner University of California, Davis Nicola Garofalo Purdue University Guanghao Hong MSRI - Mathematical Sciences Research Institute Mihaela Ifrim University of California, Berkeley Juhi Jang Cournat Institute of Mathematical Sciences Robert Jensen Loyola University Huilian Jia Xi'an Jiaotong University John King University of Florida Claudia Lederman University of Buenos Aires Ki-Ahm Lee Seoul National University Lionel Levine Massachusetts Institute of Technology Tong Li University of Iowa Erik Lindgren Norwegian University of Science and Technology Xin Yang Lu Scuola Normale Superiore Stephan Luckhaus Max-Planck-Institut for Research on Collective Goods gualdani Maria University of Texas Norayr Matevosyan University of Cambridge Henok Mawi MSRI - Mathematical Sciences Research Institute Antoine Mellet University of Maryland Regis Monneau University of Marne-la-Vallée Ricardo Nochetto University of Maryland Kaj Nyström University of Umeå John Ockendon University of Oxford

Page 8 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Betul Orcan University of Texas edouard oudet Université de Savoie (Chambéry) Yuval Peres Microsoft Research Arshak Petrosyan Purdue University Norbert Pozar University of California, Berkeley Veronica Quitalo University of Texas Ilan Roth University of California, Berkeley Sadna Sajadini Royal Institute of Technology (KTH) Lisa Maria Santos University of Minho Ovidiu Savin Columbia University Henrik Shahgholian KTH Royal Institute of Technology Wenhui Shi Purdue University Luis Silvestre University of Chicago Gieri Simonett Vanderbilt University Stephanie Somersille University of Texas Martin Strömqvist KTH Royal Institute of Technology LAN TANG University of Texas Hugo Tavares University of Lisbon Rafayel Teymurazyan University of Texas Ko Woon Um University of Iowa Nataliya Vasylyeva Institute of Applied Mathematics and Mechanics of NAS Juan Vazquez Ciudad Univ. de Canto Blanco Monica Visan University of California, Berkeley zhen wei University of Virginia Noemi Wolanski Ciudad Universitaria. Pabellon I Chunjing Xie University of Michigan Ray Yang University of Texas Yao Yao University of California, Berkeley

Page 9 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 66

Gender 66 Male 71.21% 47 Female 28.79% 19 Declined to state 0.00% 0

Ethnicity* 66 White 43.94% 29 Asian 25.76% 17 Hispanic 1.52% 1 Pacific Islander 0.00% 0 Black 4.55% 3 Native American 0.00% 0 Declined to state 24.24% 16 * ethnicity specifications are not exclusive

Page 10 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 31 100% partially 0 0% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 22 71% Satisfactory 9 29% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 12 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA Above satisfactory 19 61% Satisfactory 12 39% Not satisfactory 0 0% no opinion 0 0%

Additional comments on the topic presentation and organization Excellent Some speakers could have given more background information.

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 25 81% partially 6 19% no 0 0%

Did the workshop increase your interest in the subject? yes 30 97% partially 1 3% no 0 0%

Page 13 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA Was the workshop worth your time and effort? yes 31 100% partially 0 0% no 0 0%

Additional comments on your personal assessment Excellent talks One of the best workshops I've attended. The talks were very interesting, enlightening, and thought provoking. It was also a great group of participants to network with and discuss ...

Venue

Your overall experience at MSRI 1 - Above satisfactory 24 77% 2 6 19% 3 0 0% 4 0 0% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff

Page 14 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA 1 - Above satisfactory 27 87% 2 3 10% 3 0 0% 4 0 0% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The physical surroundings 1 -Above satisfactory 25 81% 2 5 16% 3 0 0% 4 0 0% 5 -Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 -Above satisfactory 5 16% 2 14 45% 3 11 35% 4 1 3% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Additional comments on the venue On some afternoons, sunlight blanked out the projection screen.

Thank you for completing this survey

Page 15 of 16 Free Boundary Problems, Theory and Applications, March 7, 2011 to March 11, 2011 at MSRI, Berkeley, CA, USA We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. Everything was great! A small detail: later in the afternoon the sunlight coming from one of the windows would make it hard to read the speaker's slides. It seems one of the windows is missing this ...

Number of daily responses

Page 16 of 16

Connections for Women: Arithmetic Statistics January 27, 2011 to January 28, 2011 MSRI, Berkeley, CA, USA

Organizers: Chantal David (Concordia University) Nina Snaith* (University of Bristol)

Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

REPORT ON THE ARITHMETIC STATISTICS “Connections for Women” WORKSHOP JANUARY 27‐28, 2011

Organisers: Chantal David (Concordia University) Nina Snaith (University of Bristol)

Goals of the workshop: As one of MSRI’s Connections for Women workshops, the design was to target women in fields related to the topic of the Arithmetic Statistics program, to invite them to the Connections event and then to stay on for the Introductory workshop of the program the following week. In many areas of mathematics women are still very much underrepresented and one purpose of this short workshop was to encourage as many women as possible to participate in the remainder of the program. We aimed in these two days to present overviews of the most exciting and current research areas connected with the Arithmetic Statistics program. In addition, events like this that focus on women in mathematics provide invaluable opportunities for women, particularly those in early stages of their career, to make contact with other researchers in their field.

Organisation:

There were six talks by female mathematicians over two days. The speakers were chosen so as to represent senior women as well as younger researchers, but the caliber of the speakers and their work was uniformly high.

One afternoon was set aside for a discussion session on pursuing a mathematical career. The speakers were all asked to lend their perspectives to the discussion, as well as other senior women such as Estelle Basor and Audrey Terras. The format was informal and all participants sat in a circle, introduced themselves at the beginning and were encouraged to ask questions or present topics for discussion. The topics that emerged in the initial discussion were written on the board and were all addressed during the afternoon.

Page 2 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Results:

Scientific: The workshop can boast of six very well-received talks. In the first talk, Alice Silverberg presented an overview on results on the rank of elliptic curves, from the various aspects: results on the analytic rank in families of twists, conjectures and heuristics for rank in families coming from random matrix theory, and the new spectacular results of Bhargava and Shankar bounding the average algebraic rank of elliptic curves over the rationals. In the afternoon, Alina Cojocaru discussed various questions related to the properties of reductions to the finite fields for all the primes of a fixed elliptic curve over the rationals, as the conjectures of Lang and Trotter which predicts the number of reductions with points for a fixed , or the number of reductions with a fixed ring of homormorphism, and the conjecture of Koblitz which predicts the number of reductions with a prime number of points. On the second day, Melanie Wood talked about counting number fields, and how the various ways of counting (by discriminant, by conductor, or otherwise) can affect the result. She presented some results which seem to indicate that counting by conductor is more natural:for the case of abelian extension, the various splitting type will then occur with the natural probabilities, and with the desired independence between the probabilities. Chantal David gave a review of statistics of the Riemann zeta function and other L-functions, and the connection with random matrix theory which can be seen from the fact that many statistics on the zeroes of zetafunctions match perfectly the statistics on the eigenvalues of random matrices. As an application, she explained how can one use this analogy to predict asymptotic for the vanishing of L-functions in families. Kristin Lauter discussed how many hard problems in number theory have arisen from applications in cryptography, inspiring new directions and techniques for mathematical research. The hardness of factoring integers has of course been intensely studied over the last decades, but many other cryptographic constructions involve interesting number theory, such as elliptic divisibility sequences, the Tate-Shaferevich group, Stark's conjectures, the Hecke graphs, Weil pairings, etc. Finally, Alina Bucur discussed the distribution of the number of points for some families of curves over a finite field . Random Matrix Theory makes predictions about the statistics for such families in the large limit when the genus is fixed, and she presented in her talk some complementary statistics, when the genus varies, but the field of definition is fixed.

Page 3 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

These talks did an excellent job at introducing the topics to be focused on during the remainder of the program. In the Introductory Workshop held the following week, there were many references to the talks of the Connections workshop. The time between talks was also observed to be very productive. There were always groups of mathematicians in the common areas of the institute discussing the talks or related work. Personal and career development: Many of the participants of the Connections workshop were in early stages of their career. Just as important as the information gathered from the lectures is the chance to discuss their research and their career development with peers and more senior mathematicians. This was observed to happen naturally during the lunch and coffee breaks, but the discussion session made this a little more structured and ensured that everyone had a chance to ask questions. Interestingly, the discussion session was attended equally by male and female participants of the program. The discussion was lively but focused, and covered topics that are applicable to all mathematicians, especially those at the beginning of their career. The main topics under discussion were how to apply for first jobs and postdoctoral positions, some anecdotes about how dual-career couples have found posts in the same institution, and strategies for departments keen to increase the number of women in their faculty. With participants covering the spectrum from undergraduates to those with a long career behind them, the discussion was lively and informative. Each participant had the chance to introduce themselves and pose any questions or topics for discussion.

As is standard with MSRI Connections workshops, there was also a dinner held on the Thursday evening solely for the female participants of the workshop. As all the rest of the workshop was widely attended by the program participants, making a near equal mix of men and women, the dinner was an excellent opportunity for the female researchers to meet each other. Many women were seen starting up discussions with others they had not met before, a process that helps build up a network of support and potential advice for younger female mathematicians.

Page 4 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Estelle Basor American Institute of Mathematics Alina Bucur University of California, San Diego Alina Cojocaru University of Illinois Chantal David Concordia University Kristin Lauter Microsoft Research Alice Silverberg University of California, Berkeley Melanie Wood Stanford University

Page 5 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Schedule

Thursday, January 27, 2011

10:25AM - 10:55AM Arrival and Tea

10:55AM - 11:10AM Simons Auditorium Welcome

11:10AM - 12:10PM Simons Auditorium Alice Silverberg Distributions of Ranks of Elliptic Curves

12:10PM - 2:00PM Lunch

2:00PM - 3:30PM Simons Auditorium Estelle Basor Panel discussion

3:30PM - 4:00PM Tea

4:00PM - 5:00PM Simons Auditorium Alina Cojocaru Reductions of Elliptic Curves

Friday, January 28, 2011

9:30AM - 10:30AM Simons Auditorium Melanie Wood Counting Number Fields

10:30AM - 11:00AM Tea

11:00AM - 12:00PM Simons Auditorium Chantal David L-functions and Random Matrix Theory

12:00PM - 2:00PM Lunch

Hard Problems in Number Theory arising from 2:00PM - 3:00PM Simons Auditorium Kristin Lauter Cryptography

3:00PM - 3:30PM Tea

3:30PM - 4:30PM Simons Auditorium Alina Bucur Counting Points on Curves over Finite Fields

Page 6 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Jennifer Balakrishnan Massachusetts Institute of Technology Estelle Basor American Institute of Mathematics Lisa Berger SUNY Alina Bucur University of California, San Diego Alina Cojocaru University of Illinois Chantal David Concordia University Alyson Deines University of Washington Daniel Goldston San Jose State University Wei Ho Princeton University Duc Khiem Huynh CRM - Centre de Recherches Mathématiques Kiran Kedlaya Massachusetts Institute of Technology Andrew Knightly University of Maine Sally Koutsoliotas Bucknell University Kristin Lauter Microsoft Research Cristina Martinez Universitat Autònoma de Barcelona fatemeh mohammadi Ferdowsi University of Mashhad April Morton Cal Poly Pomona Bartosz Naskręcki Adam Mickiewicz University in Poznań Jennifer Park Massachusetts Institute of Technology Antonella Perucca K.U. Leuven Carl Pomerance Dartmouth College Kenneth Ribet University of California, Berkeley Nathan Ryan Bucknell University Gagan Sekhon University of Connecticut Alice Silverberg University of California, Berkeley Kaneenika Sinha IISER Kolkata, Mohanpur Campus Nina Snaith University of Bristol Fredrik Stroemberg TU Darmstadt Hae-Sang Sun University of California, Los Angeles Lola Thompson Dartmouth College Ila Varma Princeton University Bianca Viray University of California, Berkeley John Voight University of Vermont Jacob White Arizona State University Melanie Wood Stanford University Andrew Yang Dartmouth College

Page 7 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 36

Gender 36 Male 33.33% 12 Female 55.56% 20 Declined to state 11.11% 4

Ethnicity* 36 White 55.56% 20 Asian 27.78% 10 Hispanic 0.00% 0 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 16.67% 6 * ethnicity specifications are not exclusive

Page 8 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 18 82% partially 4 18% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 19 86% Satisfactory 3 14% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 10 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Above satisfactory 10 45% Satisfactory 11 50% Not satisfactory 0 0% no opinion 1 5%

Additional comments on the topic presentation and organization several excellent talks, but not all Talks were very well prepared and I learned a lot from them. There should have been at least one or two other talks; the limited number of talks by female speakers ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 20 91% partially 2 9% no 0 0%

Did the workshop increase your interest in the subject?

Page 11 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

yes 19 86% partially 3 14% no 0 0%

Was the workshop worth your time and effort? yes 19 86% partially 3 14% no 0 0%

Additional comments on your personal assessment I really enjoyed learning about various aspects of number theory, as well as being able to interact with other women number theorists. I felt that I had adequate preparation.

Venue

Your overall experience at MSRI

Page 12 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

1 - Above satisfactory 18 82% 2 1 5% 3 1 5% 4 2 9% 5 - Not satisfactory 0 0%

Above satisfactoryNot satisfactory

Page 13 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

The assistance provided by MSRI staff 1 -Above satisfactory 18 82% 2 2 9% 3 0 0% 4 0 0% 5 -Not satisfactory 2 9%

Above satisfactoryNot satisfactory

The physical surroundings 1 -Above satisfactory 18 82% 2 1 5% 3 2 9% 4 1 5% 5 -Not satisfactory 0 0%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 -Above satisfactory 4 18% 2 3 14% 3 8 36% 4 3 14% 5 -Not satisfactory 4 18%

Page 14 of 15 Connections for Women: Arithmetic Statistics, January 27 to 28, 2011 at MSRI, Berkeley, CA, USA

Above satisfactoryNot satisfactory

Additional comments on the venue MSRI is probably the most amazing research institute I know of. The catering should be improved The main secretary was curt with me on two occasions. The lunch food was a bit expensive. Also, I would h ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. It was a great workshop, and I hope there will be many more opportunities like this one in the future! The panel discussion should be a strictly women-only event, as the presence of males at the even ...

Number of daily responses

Page 15 of 15

Introductory Workshop: Arithmetic Statistics January 31, 2011 to February 4, 2011 MSRI, Berkeley, CA, USA

Organizers: Barry Mazur (Harvard University) Carl Pomerance (Dartmouth College) Michael Rubinstein* (University of Waterloo)

Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Manjul Bhargava Princeton University Henri Cohen Université de Bordeaux I Brian Conrey American Institute of Mathematics John Cremona University of Warwick Chantal David Concordia University Jordan Ellenberg University of Wisconsin David Farmer American Institute of Mathematics Henryk Iwaniec Rutgers University Bjorn Poonen Massachusetts Institute of Technology Karl Rubin MSRI - Mathematical Sciences Research Institute Michael Rubinstein University of Waterloo Nina Snaith University of Bristol Kannan Soundararajan Stanford University William Stein University of Washington Andrew Sutherland Massachusetts Institute of Technology Frank Thorne Stanford University Akshay Venkatesh New York University, Courant Institute John Voight University of Vermont Melanie Wood Stanford University

Page 2 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Schedule

Monday, January 31, 2011 Simons 8:55AM - 9:10AM Welcome Auditorium Introduction to asymptotics of Simons 9:10AM - 10:10AM Henri Cohen number fields, conjectures, Auditorium computation, experiments 10:10AM - 10:40AM Tea Simons 10:40AM - 11:40AM Karl Rubin Selmer groups and ranks I Auditorium Simons 11:40AM - 12:40PM Manjul Bhargava Asymptotics of number fields Auditorium 12:40PM - 2:30PM Lunch Simons Michael 2:30PM - 3:30PM Overview of NT and RMT Auditorium Rubinstein 3:30PM - 4:00PM Tea Simons The ratios conjecture and 4:00PM - 5:00PM Nina Snaith Auditorium applications

Tuesday, February 01, 2011 Simons 9:00AM - 10:00AM Karl Rubin Selmer groups and ranks II Auditorium 10:00AM - 10:30AM Tea Simons 10:30AM - 11:30AM Manjul Bhargava Asymptotics of number fields, II Auditorium Simons Counting Galois Sextic Fields by 11:30AM - 12:30PM Melanie Wood Auditorium Varying Invariants 12:30PM - 2:30PM Lunch Simons Orthogonal Ensembles and Central 2:30PM - 3:30PM Brian Conrey Auditorium Values of L-functions 3:30PM - 4:00PM Tea Simons Andrew Sutherland Hyperelliptic curves, L- 4:00PM - 5:00PM Auditorium polynomials, and random matrices

Page 3 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Reception 5:00PM - 6:00PM

Wednesday, February 02, 2011 Simons Statistics of number and function 8:30AM - 9:30AM Jordan Ellenberg Auditorium fields I Simons 9:30AM - 10:30AM Manjul Bhargava Asymptotics of elliptic curves I Auditorium 10:30AM - 11:00AM Tea Simons Finding L-Functions out of 11:00AM - 12:00PM David Farmer Auditorium Nothing Simons Computations with Hilbert 12:00PM - 1:00PM John Voight Auditorium modular forms

Thursday, February 03, 2011 Simons 9:00AM - 10:00AM Manjul Bhargava Asymptotics of elliptic curves II Auditorium 10:00AM - 10:30AM Tea Bilinear Forms over Elliptic Simons 10:30AM - 11:30AM Henryk Iwaniec Curves with a Fixed Frobenius Auditorium Field Simons Statistics of number and function 11:30AM - 12:30PM Akshay Venkatesh Auditorium fields 12:30PM - 2:15PM Lunch Simons Computing Elliptic Curves using 2:15PM - 3:15PM John Cremona Auditorium Modular Symbols 3:15PM – 3:45PM Tea UC Berkeley 4:10PM - 5:00PM Bjorn Poonen x2 + y3 = z7 60 Evans Hall

Friday, February 04, 2011 Simons Towards an analogue over 9:00AM - 10:00AM William Stein Auditorium Q(sqrt(5)) of Cremona's Tables 10:00AM - 10:30AM Tea Simons Random Maximal Isotropic 10:30AM - 11:30AM Bjorn Poonen Auditorium Subspaces and Selmer Groups 11:30AM - 12:30PM Simons Kannan Moments of L-functions

Page 4 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Auditorium Soundararajan 12:30PM - 2:30PM Lunch The distribution of the zeros of L- Simons 2:30PM - 3:30PM Chantal David functions in families over function Auditorium fields 3:30PM - 4:00PM Tea Simons 4:00PM - 5:00PM Thorne: Lower terms in counting cubic fields Auditorium

Page 5 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Jennifer Balakrishnan Massachusetts Institute of Technology Lisa Berger SUNY Manjul Bhargava Princeton University Jonathan Bober MSRI - Mathematical Sciences Research Institute alina bucur University of California Joe Buhler Institute for Defense Analyses (CCR-LJ) Suh Hyun Choi Harvard University Mirela Ciperiani University of Texas Henri Cohen Université de Bordeaux I Brian Conrey American Institute of Mathematics John Conrey American Institute of Mathematics John Cremona University of Warwick Andrew Critch University of California Chantal David Concordia University Bart de Smit Universiteit Leiden Jordan Ellenberg University of Wisconsin David Farmer American Institute of Mathematics Brooke Feigon MSRI - Mathematical Sciences Research Institute Ralph Furmaniak Stanford University Derek Garton University of Wisconsin Daniel Goldston San Jose State University Steve Gonek University of Rochester Chris Hall University of Wyoming Aloysius Helminck North Carolina State University paul herman Department of Defense Ghaith Hiary MSRI - Mathematical Sciences Research Institute Wei Ho Columbia University Duc Khiem Huynh University of Waterloo Henryk Iwaniec Rutgers University Zev Klagsbrun University of California Andrew Knightly University of Maine Sally Koutsoliotas Bucknell University Jeffrey Lagarias University of Michigan Soumendra Lahiri Texas A & M University Michel Lapidus University of California Stephen Lester University of Rochester Benjamin Levitt California State University Robert Miller MSRI - Mathematical Sciences Research Institute

Page 6 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Bartosz Naskręcki Adam Mickiewicz University Jennifer Park Massachusetts Institute of Technology Ryan Peckner Princeton University Antonella Perucca Katholieke Universiteit Leuven Ian Petrow Stanford University Carl Pomerance Dartmouth College Bjorn Poonen Massachusetts Institute of Technology Kenneth Ribet University of California xxx Rishikesh University of Waterloo Karl Rubin MSRI - Mathematical Sciences Research Institute Michael Rubinstein University of Waterloo Simon Rubinstein-Salzedo Stanford University Nathan Ryan Bucknell University Gagan Sekhon University of Connecticut Alice Silverberg University of California, Berkeley Kaneenika Sinha IISER Kolkata, Mohanpur Campus Nina Snaith University of Bristol Kannan Soundararajan Stanford University Harold Stark MSRI - Mathematical Sciences Research Institute William Stein University of Washington Fredrik Stroemberg MSRI - Mathematical Sciences Research Institute Hae-Sang Sun Chungbuk National University Andrew Sutherland Massachusetts Institute of Technology Takashi Taniguchi Princeton University Audrey Terras MSRI - Mathematical Sciences Research Institute Lola Thompson Dartmouth College Frank Thorne Stanford University Gonzalo Tornaria University of the Republic Craig Tracy University of California Enrique Trevino Dartmouth College Seyfi Turkelli University of Georgia Ronald van Luijk Universiteit Leiden Ila Varma Princeton University Akshay Venkatesh New York University, Courant Institute Bianca Viray Brown University John Voight University of Vermont Paul Vojta University of California Jamie Weigandt Purdue University

Page 7 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Jacob White MSRI - Mathematical Sciences Research Institute Kevin Wilson Princeton University Melanie Wood Stanford University Shuntaro Yamagishi University of Waterloo Andrew Yang Dartmouth College

Page 8 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 81

Gender 81 Male 69.14% 56 Female 23.46% 19 Declined to state 7.41% 6

Ethnicity* 81 White 58.02% 47 Asian 17.28% 14 Hispanic 3.70% 3 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 20.99% 17 * ethnicity specifications are not exclusive

Page 9 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 34 85% partially 5 13% no 1 3% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 33 83% Satisfactory 7 18% Not satisfactory 0 0% no opinion 0 0%

Was there adequate time between lectures for discussion?

Page 11 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Above satisfactory 13 33% Satisfactory 17 43% Not satisfactory 10 25% no opinion 0 0%

Additional comments on the topic presentation and organization Way too many talks It's not so clear to me that Cohen-Lenstra and random matrices will be a good pairing for the semester, merely on the basis that they both use statistics. Brilliant programme! It wou ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 34 85% partially 6 15% no 0 0%

Did the workshop increase your interest in the subject?

Page 12 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

yes 35 88% partially 5 13% no 0 0%

Was the workshop worth your time and effort? yes 37 93% partially 3 8% no 0 0%

Additional comments on your personal assessment This was a wonderful academic experience - to see the latest results in the area presented by lead researchers. Many of the speakers did an excellent job of providing the background necessary to foll ...

Venue

Your overall experience at MSRI

Page 13 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

1 - Above satisfactory 24 60% 2 12 30% 3 2 5% 4 1 3% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

Page 14 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

The assistance provided by MSRI staff 1 -Above satisfactory 23 57% 2 11 28% 3 4 10% 4 0 0% 5 -Not satisfactory 2 5%

Above satisfactoryNot satisfactory

The physical surroundings 1 -Above satisfactory 32 80% 2 5 13% 3 1 3% 4 0 0% 5 -Not satisfactory 2 5%

Above satisfactoryNot satisfactory

The food provided during the workshop 1 -Above satisfactory 7 18% 2 11 28% 3 14 35% 4 5 13% 5 -Not satisfactory 3 8%

Page 15 of 16 Introductory Workshop: Arithmetic Statistics, January 31, 2011 to February 4, 2011 at MSRI, Berkeley, CA, USA

Above satisfactoryNot satisfactory

Additional comments on the venue No vegan food options were available The lack of food is a big problem. The catering should be improved The lecture room was always either much too hot or much too cold. Fixing this needs to be made a ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. The lecture room was always either much too hot or much too cold. Fixing this needs to be made a higher priority. Outstanding. The best conference I've ever been to. I had a wonderful experience at th ...

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Page 16 of 16

Arithmetic Statistics April 11, 2011 to April 15, 2011 MSRI, Berkeley, CA, USA

Organizers: Brian Conrey (American Institute of Mathematics) Barry Mazur (Harvard University) Michael Rubinstein* (University of Waterloo) Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Report on Topical Workshop: Arithmetic Statistics April 11 – 15, 2011 Submitted by Barry Mazur

ORGANIZATIONAL STRUCTURE The organizational structure of this workshop follows the pattern of the organization of the program itself, which I see as having three (interlocking) parts: (1) Actual Computation (2) Estimation (3) Number theoretic (structural) issues directly related to the above

SCIENTIFIC GOALS The goal of our workshop was to highlight this, describing the mathematics that was being developed in our program, or was of fundamental importance for our program. In fact, much of the roster of talks presented new—usually still on-going—work developed or worked on here at MSRI during our program. To give you an explicit run-down of the talks, here is a catalogue raisonn´e, with commentary to follow:

(1) Computing

(a) Ghaith Hiary: Fast methods to compute the Riemann zeta function (b) Kiran Kedlaya: Computing Zeta Functions of Curves with Automorphisms (c) Andrew Booker: Maass forms and class groups

(2) Estimating

(a) Manjul Bhargava: A positive proportion of plane cubics fail the Hasse principle (b) Wei Ho: Bounding Average Ranks of Elliptic Curves in Families (c) Par Kurlberg: Point count statistics for families of curves over ﬁnite ﬁelds (d) Henryk Iwaniec: The Riemann Hypothesis is more likely to be true than not! (e) Alina Cojocaru: Almost all reductions of a generic Drinfeld module have a large exponent (f) Barry Mazur: Disparity in the statistics for quadratic twist families of elliptic curves (g) Jon Keating: Large values of the zeta function and disordered landscapes

(3) Structural Issues

(a) Alice Silverberg: Elliptic curves with a 7-isogeny, and a recalcitrant genus 12 curve (b) Nathan Jones: Images of Galois representations associated to elliptic curves (c) Gonzalo Tornaría: Paramodular forms and B¨ocherer’s Conjecture (d) Nils-Peter Skoruppa: Towards an arithmetic theory of Jacobi forms over number ﬁelds (e) David (Roger) Heath-Brown: Powers as values of polynomials

Page 2 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

The talks above weave together, and many of them had their underlying mathematics developed during the conference—or, at least, during the time of the conference.

• Alice Silverberg’s talk described a result largely developed during our conference with very signiﬁcant help from computations of Michael Rubinstein, Drew Sutherland and Jennifer Balakrishnan and theoretical help from Karl Rubin and others here. That project (which has half a dozen co-authors) also found common ground with problems described in the talks of Nathan Jones and Alina Cojocaru, during the workshop itself.

• The talk of Iwaniec described work done by him and his coauthors right here at MSRI during our program in just days before the workshop. This also is a striking example of the success of the program: that group had as their goal to prove that, as the title of Iwaniec’s talk says, “The Riemann Hypothesis is more than half true.”

• My talk consisted entirely of material developed during the program (with my co-authors Zev Kalgsbrun and Karl Rubin The subject of my talk also connects—in its subject matter—with the talks of Manjul Bhargava and Wei Ho. Bhargava and Ho (and Melanie Wood, who spoke in our introductory workshop) are in the midst of a magniﬁcent large project that kept getting better and better results day after day during the time of our program.

FUNDING GUIDELINES In determining funding, a preference was given to graduate students, postdocs, junior researchers, and mathematicians from under-represented groups. Because a number of our speakers were members of our programs, we were able to allocate more funds to them. There were 29 funded participants.

ASSESSMENT OF ITS SUCCESS AND SPECIFIC ACCOMPLISHMENTS I do think that it was wonderful: the out-of-the-ordinary level of cohesiveness established between sub-communities of mathematicians (people coming from the computing world, from the analytic number theoretic world, and from the more algebraic-minded world) as they saw their problems part of a larger uniﬁed fabric, was terriﬁc.

Page 3 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Manjul Bhargava Princeton University Andrew Booker University of Bristol Alina Carmen Cojocaru University of Illinois Rogewr Heath-Brown University of Oxford Ghaith Hiary MSRI - Mathematical Sciences Research Institute Wei Ho Columbia University Henryk Iwaniec Rutgers University Nathan Jones University of Mississippi Jonathan Keating University of Bristol Kiran Kedlaya Massachusetts Institute of Technology Par Kurlberg Royal Institute of Technology (KTH) Barry Mazur Harvard University Alice Silverberg University of California, Berkeley Nils Skoruppa Universität Siegen Gonzalo Tornaria University of the Republic

Page 4 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Schedule

Monday, April 11, 2011 9:25AM - 9:40AM Simons Auditorium Welcome The Riemann Hypothesis is more likely to be true than not! 9:40AM - 10:30AM Simons Auditorium Iwaniec

10:30AM - 11:10AM Atrium Tea Point count statistics for families of curves over 11:10AM - 12:00PM Simons Auditorium Par Kurlberg finite fields 12:00PM - 2:10PM Atrium Lunch Manjul A positive proportion of plane cubics fail the Hasse 2:10PM - 3:00PM Simons Auditorium Bhargava principle 3:00PM - 3:30PM Atrium Tea Images of Galois representations associated to 3:30PM - 4:20PM Simons Auditorium Nathan Jones elliptic curves 4:20PM - 6:00PM Atrium Reception Tuesday, April 12, 2011 Alina Almost all reductions of a generic Drinfeld module have a 9:40AM - 10:30AM Simons Auditorium Cojocaru large exponent 10:30AM - 11:10AM Atrium Tea 11:10AM - 12:00PM Simons Auditorium Jon Keating Large values of the zeta function and disordered landscapes 12:00PM - 2:10PM Atrium Lunch Gonzalo 2:10PM - 3:00PM Simons Auditorium Paramodular forms and Böcherer's Conjecture Tornaría 3:00PM - 3:30PM Atrium Tea Wednesday, April 13, 2011 Disparity in the statistics for quadratic twist families of 9:40AM - 10:30AM Simons Auditorium Barry Mazur elliptic curves 10:30AM - 11:10AM Atrium Tea Fast methods to compute the Riemann zeta function 11:10AM - 12:00PM Simons Auditorium Ghaith Hiary

Page 5 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Thursday, April 14, 2011 Nils-Peter Towards an arithmetic theory of Jacobi forms over number 9:40AM - 10:30AM Simons Auditorium Skoruppa fields 10:30AM - 11:10AM Atrium Tea Alice Elliptic curves with a 7-isogeny, and a recalcitrant genus 12 11:10AM - 12:00PM Simons Auditorium Silverberg curve 12:00PM - 2:10PM Atrium Lunch David 2:10PM - 3:00PM Simons Auditorium (Roger) Powers as values of polynomials Heath-Brown 3:00PM - 3:30PM Atrium Tea Friday, April 15, 2011 9:40AM - 10:30AM Simons Auditorium Wei Ho Bounding Average Ranks of Elliptic Curves in Families 10:30AM - 11:10AM Atrium Tea Andrew 11:10AM - 12:00PM Simons Auditorium Maass forms and class groups Booker 12:00PM - 2:10PM Atrium Lunch Kiran 2:10PM - 3:00PM Simons Auditorium Computing Zeta Functions of Curves with Automorphisms Kedlaya 3:00PM - 3:30PM Atrium Tea

Page 6 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Matthew Alderson University of Waterloo Jennifer Balakrishnan Massachusetts Institute of Technology Helene Barcelo Arizona Western College Mhamoudrez Bazarganzadeh Stockholm University Matthias Beck San Francisco State University Sandro Bettin University of Bristol Manjul Bhargava Princeton University Jean-François Biasse University of Calgary Jonathan Bober MSRI - Mathematical Sciences Research Institute Andrew Booker University of Bristol Hatice Boylan Universität Siegen Alina Bucur University of California, Berkeley Joe Buhler Institute for Defense Analyses (CCR-LJ) Vorrapan Chandee Stanford University Henri Cohen Université de Bordeaux I Alina Carmen Cojocaru University of Illinois Brian Conrey American Institute of Mathematics John Cremona University of Warwick Gabriele Dalla Torre Universiteit Leiden Giuliana Davidoff Mount Holyoke College Lassina Dembele University of Warwick Anne-Maria Ernvall-Hytönen University of Turku David Farmer American Institute of Mathematics Brooke Feigon MSRI - Mathematical Sciences Research Institute Ralph Furmaniak Stanford University Rogewr Heath-Brown University of Oxford Aloysius Helminck North Carolina State University Ghaith Hiary MSRI - Mathematical Sciences Research Institute Wei Ho Columbia University Samuel Holmin Royal Institute of Technology (KTH) Duc Khiem Huynh University of Waterloo Henryk Iwaniec Rutgers University Nathan Jones University of Mississippi Jonathan Keating University of Bristol Kiran Kedlaya Massachusetts Institute of Technology Hershy Kisilevsky Concordia University

Page 7 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Sally Koutsoliotas Bucknell University Abhinav Kumar Massachusetts Institute of Technology Par Kurlberg Royal Institute of Technology (KTH) Jeffrey Lagarias University of Michigan Miichel Lapidus University of California, Berkeley Stefan Lemurell Chalmers University of Technology/University of Göteborg Hendrik Lenstra Universiteit Leiden Barry Mazur Harvard University Somayeh Moazeni University of Waterloo Bogdan Petrenko State University College, SUNY Carl Pomerance Dartmouth College Robert Rhoades Stanford University Kenneth Ribet University of California, Berkeley .xxx Rishikesh University of Waterloo Brad Rodgers University of California, Berkeley Michael Rubinstein University of Waterloo Simon Rubinstein-Salzedo Stanford University Sam Ruth Princeton University Nathan Ryan Bucknell University Sadna Sajadini Royal Institute of Technology (KTH) Gagan Sekhon University of Connecticut Mehmet Haluk Sengun University of Barcelona Alice Silverberg University of California, Berkeley Kaneenika Sinha IISER Kolkata, Mohanpur Campus Nils Skoruppa Universität Siegen Anders Södergren Institute for Advanced Study Harold Stark MSRI - Mathematical Sciences Research Institute Fredrik Stroemberg MSRI - Mathematical Sciences Research Institute Lenny Taelman Universiteit Leiden Nicolas Templier Princeton University Gonzalo Tornaria University of the Republic Henrik Ueberschaer Tel Aviv University Ila Varma Princeton University John Voight University of California, Berkeley Jamie Weigandt Purdue University Jared Weinstein University of California, Berkeley

Page 8 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participants First Name Last Name Current Institution Kevin Wilson Princeton University Melanie Wood Princeton University Shuntaro Yamagishi University of Waterloo Peng Zhao Princeton University

Page 9 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 76

Gender 76 Male 64.47% 49 Female 21.05% 16 Declined to state 14.47% 11

Ethnicity* 76 White 60.53% 46 Asian 14.47% 11 Hispanic 1.32% 1 Pacific Islander 0.00% 0 Black 1.32% 1 Native American 0.00% 0 Declined to state 22.37% 17 * ethnicity specifications are not exclusive

Page 10 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 25 71% partially 10 29% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 20 57% Satisfactory 15 43% Not satisfactory 0 0% no opinion 0 0%

Page 12 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Was there adequate time between lectures for discussion? Above satisfactory 30 86% Satisfactory 5 14% Not satisfactory 0 0% no opinion 0 0%

Additional comments on the topic presentation and organization Wonderful topics! Thanks!! The Cohen-Lenstra heuristics are a central instance of "statistics" popping up in number theory, and I was surprised at how little of this workshop dealt with that.

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 26 74% partially 9 26% no 0 0%

Page 13 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Did the workshop increase your interest in the subject? yes 26 74% partially 7 20% no 2 6%

Was the workshop worth your time and effort? yes 34 97% partially 1 3% no 0 0%

Additional comments on your personal assessment I learn a lot from the workshop and talking with other colleagues.

Venue

Page 14 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Your overall experience at MSRI 1 - Above satisfactory 24 69% 2 9 26% 3 0 0% 4 1 3% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff 1 - Above satisfactory 21 60% 2 8 23% 3 4 11% 4 1 3% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The physical surroundings 1 - Above satisfactory 28 80% 2 3 9% 3 2 6% 4 2 6% 5 - Not satisfactory 0 0%

Page 15 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Above satisfactoryNot satisfactory

The food provided during the workshop 1 - Above satisfactory 8 23% 2 8 23% 3 13 37% 4 3 9% 5 - Not satisfactory 3 9%

Above satisfactoryNot satisfactory

Additional comments on the venue Excellent experience! More (labeled!) vegan options would be welcomed. I did not buy the lunches so cannot comment on those

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. Thank you very much for organizing such a wonderful workshop!

Number of daily responses

Page 16 of 17 Arithmetic Statistics, April 11, 2011 to April 15, 2011 at MSRI, Berkeley, CA, USA

Page 17 of 17

Hot Topics: Kervaire invariant October 25, 2010 to October 29, 2010 MSRI, Berkeley, CA, USA

Organizers: Mike Hill (University of Virginia) Michael Hopkins (Harvard University) Douglas C. Ravanel* (University of Rochester)

Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

Organizers • Michael Hill (University of Virginia) • Michael Hopkins (Harvard University) • Douglas Ravenel (University of Rochester)

1. Scientific Description In April 2009, Hill-Hopkins-Ravenel announced a solution to the Kervaire In- variant One problem. This resolved an almost 50 year old problem in topology, and their techniques and approach was quite different than anything previously attempted: they related the homotopical formulation due to Browder to equivariant homotopy computations. While one of the oldest branches of algebraic topology, equivariant homotopy theory (homotopy theory done in spaces endowed with an action of a fixed group G) is also one of the least understood. Many computations viewed as routine or now elementary are simply unknown in the equivariant case, even for simple groups G. One of the primary goals of the workshop was to render less esoteric and scary this rich branch of algebraic topology, and many participants left knowing that computations equivariantly are much more tractable than previously thought. While the workshop focused primarily on the equivariant methods, a few talks were also dedicated to linking these computations to the classical Kervaire Invariant One problem. The connection relies on a theorem of Browder: Kervaire Invariant One manifolds are detected by a particular family of elements in the classical Adams spectral sequence. These elements all live in dimensions 2 less than a power of 2, and the hypothetical homotopy element representing a Kervaire Invariant One element j+1 in dimension 2 − 2 is usually denoted θj. The Hill-Hopkins-Ravenel result then says that for j ≥ 7, θj does not exist. This workshop served as a detailed reading and analysis of the proof. While Hill-Hopkins-Ravenel gave several talks, the majority of talks were given by people not involved in the project. This increased the familiarity of workers in algebraic topology with both the classical techniques in equivariant homotopy and the new tools developed to solve the Kerviare problem. The talks therefore ran the gamut in terms of complexity and detail: some served as general discussions of the underlying theory while others focused on key features of specific computations. This itself showed the breadth of equivariant homotopy, reengaging many participants with equivariant homotopy theory.

2. Highlights of the Presentations The workshop started with a pair of talks given by John Jones (Warwick) about the history of the Kervaire Invariant One problem and the connections to other aspects of topology. In particular, he described the construction of the known Kervaire classes, linked the homotopical story of the conference with the classical geometric story dating back to the 1930s, and described some of the conjectures and consequences surrounding the now known non-existence of the Kervaire classes. Doug Ravenel gave a broad-strokes overview of the proof, explaining the general connections between each of the subsequent talks. In particular, he stressed from the beginning the importance of equivariant homotopy (Talks 4 & 5), the slice ﬁltration (Talks 6 & 15), computations of equivariant homology groups (Talks 5 & 1

Page 2 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

7), and the analysis of differentials in the slice spectral sequence (Talks 8 & 13). Ravenel also described the norm functor (Talk 9) and the spectrum MU (G) (Talk 10). The next few talks provided a foundation for equivariant homotopy theory and computations therein. Peter May (University of Chicago) gave a brief survey of the model categorical background and some of the subtleties of the particular model of equivariant homotopy used in the proof. He also introduced the foundational tool of geometric fixed points. John Greenlees (University of Sheffield) continued the discussion of geometric fixed points and isotropy separation. He also described the conceptual underpinnings of Bredon [co]homology, introducing Mackey functors and the chain complexes used to compute homology groups. Mike Hill (University of Virginia) then described the “Slice Theorem” and the “Slice Tower”. This tied the necessary computations for the proof to the general homological discussion presented by Greenlees. Teena Gerhardt (Michigan State University) continued in this vein, introducing effective chain complexes which allowed for easy computations of the homology groups which appear in the proof. She also proved the “Gap Theorem”, one of the key steps in the broader proof. Igor Kriz (University of Michigan) then completed the subsection on computations, described what happens for the group C2. At this stage, the lectures focused slightly more on the specifics of MU (G). Haynes Miller (MIT) gave a general talk about the norm functor. He described it in very general terms, and this allowed a nice description of the interactions between slices and MU (G). Nitu Kitchloo (Johns Hopkins) tied Miller’s discussion of the norm and MU (G) to formal groups, describing the particularly nice choice of generators of the homotopy of MU (G) that appear in the slice theorem. This tied back to Hill’s talk, allowing for easier understanding of the statement of the slice theorem. Talks 11 and 12 focused on the “Detection Theorem”: the extraordinary cohomology theory constructed by Hill-Hopkins-Ravenel faithfully sees the Kervaire classes. Mark Behrens (MIT) spoke on Ravenel’s proof of the odd-primary Kervaire Invariant. He recast Ravenel’s original argument into modern language, and very cleanly set the stage for the two-primary arguement. Doug Ravenel (University of Rochester) then described the proof of the “Detection Theorem”. This linked computations doable in the late 1970s with the equivariant machinery used in the other parts of the proof. Talks 13 and 14 are closely related: they describe differentials in the Slice Spec- tral Sequence and the very important consequence that the distinct functors “fixed points” and “homotopy fixed points” agree for the Hill-Hopkins-Ravenel spectrum. Po Hu (Wayne State University) gave a detailed talk which linked the underlying geometric picture (the geometric fixed points of MU (G) is MO, the unoriented bordism spectrum) to differentials in the slice spectral sequence. This resulted in a complete description of the differentials in a range, and moreover, she used this computation to prove the “Periodicity Theorem”. Andrew Blumberg (University of Texas at Austin) derived from these computations the “Homotopy Fixed Points” theorem, showing that for a very general class of equivariant spectra (to which the Hill-Hopkins-Ravenel spectrum belongs), the fixed and homotopy fixed points functors coincide. This completed the proof of the Kervaire theorem, modulo the proof that the slices of MU (G) are as claimed.

Page 3 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

Talks 15, 16, & 17 were by far the most technical. Dan Dugger (University of Oregon) began by describing how to derive the “Slice Theorem” from an apparently simpler result, the “Reduction Theorem”. This has a classical form: if you kill all of the generators of a polynomial algebra over a ring, then you recover the ring, and the version non-equivariantly is due to Quillen. In the equivariant case, this is the most diﬃcult part of the paper. Mike Hill (UVA) picked up here and described the general inductive framework used to prove the reduction theorem. He then showed how to reduce the entire argument to checking that a single map between 1-dimensional vector spaces over F2 is non-zero. Mike Hopkins (Harvard) then proved that this map is the identity. He also described a geometric approach which would greatly simplify the proof of the Reduction Theorem and which harkens back to the earlier geometric underpinnings of the problem. This concluded the workshop.

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Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

Schedule Monday, October 25, 2010 9:25AM - 9:40AM Welcome 9:40AM - 10:40AM John Jones History of the Kervaire Invariant One Problem 10:40AM - 11:10AM Tea 11:10AM - 12:10PM John Jones Construction of the Kervaire Classes 12:10PM - 2:00PM Lunch 2:00PM - 3:00PM Douglas Ravenel An Overview of the proof 3:00PM - 3:30PM Tea 3:30PM - 4:30PM J. May Introduction to Equivariant Homotopy I 4:30PM - 5:50PM Reception Tuesday, October 26, 2010 9:30AM - 10:30AM John Greenlees Introduction to Equivariant Homotopy II 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Michael Hill Introduction to the Slice Tower: The Slice Theorem 12:00PM - 2:00PM Lunch 2:00PM - 3:00PM Teena Gerhardt The Homology of Slice Cells: the Gap Theorem 3:00PM - 3:30PM Tea 3:30PM - 4:30PM Igor Kriz The Slice Spectral Sequence for $C_2$ and $C_4$ Wednesday, October 27, 2010 9:30AM - 10:30AM Haynes Miller The norm functor and $MU^{((G))}$ 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Nitya Kitchloo Distinguished Classes in the Underlying Homotopy of $MU^{((G))}$ 4:10PM – 5:00PM Michael Hopkins Bowen Lecture II @ 50 Birge Hall, UC Berkeley Thursday, October 28, 2010 9:00AM - 10:00AM Mark Behrens Introduction to the Adams-Novikov Spectral Sequence: Ravenel\'s Proof for Primes > 3 10:00AM - 10:30AM Tea 10:30AM - 11:30PM Douglas Ravenel Proof of the Detection Theorem 11:30PM - 12:30PM Po Hu Differentials in the Slice Spectral Sequence: the Periodicity Theorem 12:30PM - 2:00PM Lunch 2:00PM – 3:00PM Michael Hopkins, Micheal Q & A Session Hill, Douglas Ravenel 3:00PM – 3:30PM Tea 4:10PM – 5:00PM Michael Hopkins Bowen Lecture III @ 50 Birge Hall, UC Berkeley Friday, October 29, 2010 9:30AM - 10:30AM Andrew Blumberg The Homotopy Fixed Points Theorem 10:30AM - 11:00AM Tea 11:00AM - 12:00PM Daniel Dugger From the Reduction Theorem to the Slice Theorem 12:00PM - 2:00PM Lunch 2:00PM - 3:00PM Michael Hill Proof of the Reduction Theorem I 3:00PM - 3:30PM Tea 3:30PM - 4:30PM Michael Hopkins Proof of the Reduction Theorem II

Page 5 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

Invited Speakers First Name Last Name Current Institution Mark Behrens Massachusetts Institute of Technology Andrew Blumberg Stanford University Daniel Dugger University of Oregon Teena Gerhardt Michigan State University John Greenlees University of Sheffield Micheal Hill University of Virginia Michael Hopkins Harvard University Po Hu Wayne State University John Jones Arizona State University Nitya Kitchloo Johns Hopkins University Igor Kriz University of Michigan J. May University of Chicago Haynes Miller MIT Douglas Ravenel University of Rochester

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Officially Registered Participants First Name Last Name Current Institution Michal Adamaszek University of Warwick Maia Averett Mills College Mark Behrens Massachusetts Institute of Technology Julie Bergner University of California Andrew Blumberg Stanford University Irina Bobkova Northwestern University Anna Marie Bohmann University of Chicago Jonathan Campbell Stanford University Man Chuen Cheng Stanford University Daniel Dugger University of Oregon Bjorn Dundas University of Bergen William Dwyer Department of Mathematics Soren Galatius Stanford University Ana Garcia-Pulido University of Warwick Teena Gerhardt Michigan State University John Greenlees University of Sheffield Ilya Grigoriev Stanford University Bertrand Guillou University of Illinois at Urbana-Champaign Micheal Hill University of Virginia Michael Hopkins Harvard University Po Hu Wayne State University John Jones Arizona State University Nitya Kitchloo Johns Hopkins University Igor Kriz University of Michigan Don Larson University of Rochester Cary Malkiewich Stanford University J. May University of Chicago Haynes Miller MIT Fatemeh Mohammadi Ferdowsi University of Mashhad Aniceto Murillo University of Málaga Tracy Nance Stanford University Douglas Ravenel University of Rochester Hal Sadofsky University of Oregon Rekha Santhanam Johns Hopkins University Marco Schlichting Louisiana State University Nathaniel Stapleton Indiana University Vesna Stojanoska Northwestern University Rupert Swarbrick University of Warwick Paul Synhavsky University of Rochester Dylan Wilson University of Washington Miguel Xicotencatl Centro de Investigacion y de Estudios Avanzados del IPN

Page 7 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

Officially Registered Participant Information Participants 41

Gender 41 Male 63.41% 26 Female 21.95% 9 Declined to state 14.63% 6

Ethnicity* 41 White 58.54% 24 Asian 9.76% 4 Hispanic 2.44% 1 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 29.27% 12 * ethnicity specifications are not exclusive

Page 8 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA

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Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 32 100% partially 0 0% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? Above satisfactory 26 81% Satisfactory 4 13% Not satisfactory 0 0% no opinion 2 6%

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Page 10 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA Above satisfactory 19 59% Satisfactory 12 38% Not satisfactory 0 0% no opinion 1 3%

Additional comments on the topic presentation and organization Great choice of speakers Amazing workshop - I learned so much The first day had several survey lectures. It would have been better if one or two of those were postponed until the fourth day. Great! It ...

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Was your background adequate to access a reasonable portion of the material? yes 24 75% partially 8 25% no 0 0%

Did the workshop increase your interest in the subject? yes 30 94% partially 1 3% no 1 3%

Page 11 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA Was the workshop worth your time and effort? yes 32 100% partially 0 0% no 0 0%

Additional comments on your personal assessment Again, great! During the talks I got several references that will be very useful in my current work The workshop was superb; I came away feeling like I had a good grasp on the contours of the entire p ...

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Page 12 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA 1 - Above satisfactory 25 78% 2 5 16% 3 2 6% 4 0 0% 5 - Not satisfactory 0 0%

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Additional comments on the venue Great place for a conference Great! MSRI is a mathematical fairy- land. The lunches at MSRI are terrible (to my, quite picky) taste) The building, auditorium and vista are absolutely beautiful! the MSRI f ...

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Page 13 of 14 Hot Topics: Kervaire invariant, October 25, 2010 at MSRI, Berkeley, CA, USA We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants.

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Page 14 of 14

SIAM/MSRI workshop on Hybrid Methodologies for Symbolic-Numeric Computation November 17, 2010 to November 19, 2010 MSRI, Berkeley, CA, USA

Organizers: Mark Giesbrecht (University of Waterloo) Erich Kaltofen* (North Carolina State University) Daniel Lichtblau (Wolfram Research) Seth Sullivant (North Carolina State University) Lihong Zhi (Chinese Academy of Sciences, Beijing)

Schedule

Wednesday, November 17, 2010 9:00AM - 9:25AM Opening 9:25AM - 10:15AM Bernd Sturmfels Introduction to Convex Algebraic Geometry 10:15AM - 10:45AM Tea 10:45AM - 11:10AM Philipp Rostalski Bermeja - Software for Convex Algebraic Geometry Jonathan 11:10AM - 12:00PM Deflation and most singular set Hauenstein 12:00PM - 1:30PM Lunch Decay properties of matrix functions: an application to electronic structure 1:30PM - 2:20PM Paola Boito computation Geometric symbolic-numeric methods for differential and algebraic 2:20PM - 3:10PM Gregory Reid equation 3:10PM - 3:45PM Tea 3:45PM - 4:10PM John May Applying Approximate Decomposition to Polynomial Root Finding Roger 4:10PM - 5:00PM Talk Germundsson Thursday, November 18, 2010 Computer-assisted existence and multiplicity proofs for elliptic boundary 9:00AM - 9:50AM Michael Plum value problems Orbital stability investigations for travelling waves in a nonlinearly 9:50AM - 10:15AM Kaori Nagatou supported beam 10:15AM - 10:45AM Tea 10:45AM - 11:10AM Wen-shin Lee Searching for Sparsity 11:10AM - 12:00PM Charles Wampler Finding Exceptional Sets via Regenerative Fiber Products 12:00PM - 1:30PM Lunch 1:30PM - 1:55PM Damien Stehle A numerically stable LLL reduction 1:55PM - 2:20PM Andy Novocin Towards L1, a quasi-linear LLL 2:20PM - 3:10PM Tanush Shaska Numerical Methods in Algebraic Geometry 3:10PM - 3:45PM Tea 3:45PM - 4:10PM Zhengfeng Yang Blind Image Deconvolution via Fast Approximate GCD Symbolic and symbolic-numeric techniques for dynamical modeling and 4:10PM - 5:00PM Jürgen Gerhard simulation Friday, November 19, 2010 MARK 9:00AM - 9:50AM Hybrid methods for Composition and Splitting SOFRONIOU 9:50AM - 10:15AM Hirokazu Anai A symbolic-numeric approach to nonlinear dynamical system analysis 10:15AM - 10:45AM Tea 10:45AM - 11:10AM Daniel Bates Numerical consequences of symbolic choices in Gale Duality Mohab Safey El On Applications of Quantifier Elimination to LMI and the Stability Region 11:10AM - 12:00PM Din of Numerical Schemes 12:00PM - 1:30PM Lunch 1:30PM - 1:55PM Anton Leykin Certified numerical homotopy tracking Computing the radius of positive semidefiniteness of a multivariate real 1:55PM - 2:20PM Sharon Hutton polynomial via a dual of Seidenberg's method 2:20PM - 3:10PM Jan Verschelde Quality Up in Polynomial Homotopy Continuation 3:10PM - 3:45PM Tea 3:45PM - 4:45PM Ilse Ipsen Panel discussion

Speakers

First Name Last Name Current Institution Hirokazu Anai Fujitsu laboratoried ltd Daniel Bates Colorado State University Centre Européen de Recherche et de Formation Paola Boito Avancée en Calcul Scientifique (CERFACS) Jürgen Gerhard Maplesoft Roger Germundsson Wolfram Research Jonathan Hauenstein Texas A&M Sharon Hutton North Carolina State University Ilse Ipsen North Carolina State University Wen-shin Lee Universiteit Antwerp Anton Leykin Georgia Institute of Technology John May Maplesoft Kaori Nagatou Kyushu University Andy Novocin École Normale Supérieure de Lyon Michael Plum KIT (University of Kalrsruhe) Gregory Reid University of Western Ontario Philipp Rostalski University of California Mohab Safey El Din Université de Paris VI (Pierre et Marie Curie) Tanush Shaska Oakland University Mark Sofroniou Wolfram Research Damien Stehle École Normale Supérieure de Lyon Bernd Sturmfels University of California, Berkeley Jan Verschelde University of Illinois at Chicago Charles Wampler General Motors Research and Development Center Zhengfeng Yang Shanghai Key Lab of Trustworthy Computing Officially Registered Participants

First Name Last Name Current Institution Hirokazu Anai Fujitsu laboratoried ltd Dennis Arnon IBM Guy Baruch California Institute of Technology Daniel Bates Colorado State University Lubjana Beshaj University of Vlora Centre Européen de Recherche et de Formation Paola Boito Avancée en Calcul Scientifique (CERFACS) Michael Burr Fordham University Barry Dayton Northeastern Illinois University Gabriel Dos Reis Texas A & M University Richard Fateman University of California Jürgen Gerhard Maplesoft Roger Germundsson Wolfram Research Mark Giesbrecht University of Waterloo Jonathan Hauenstein Texas A&M Sharon Hutton North Carolina State University Ilse Ipsen North Carolina State University Erich Kaltofen North Carolina State University Robert Korsan none George Labahn University of Waterloo Wen-shin Lee Universiteit Antwerp Lutz Lehmann Humboldt-Universität Anton Leykin Georgia Institute of Technology Daniel Lichtblau Wolfram Research John May Maplesoft Perrin Meyer Rockefeller University Fatemeh Mohammadi MSRI Nathan Moshman Naval Postgraduate School Kaori Nagatou Kyushu University Andy Novocin École Normale Supérieure de Lyon Hyungju Park University of Illinois, Urbana Michael Plum KIT (University of Kalrsruhe) Gregory Reid University of Western Ontario Philipp Rostalski University of California Mohab Safey El Din Université de Paris VI (Pierre et Marie Curie) Raman Sanyal University of California, Berkeley Tanush Shaska Oakland University Mark Sofroniou Wolfram Research Pierre-Jean Spaenlehauer Université de Paris VI (Pierre et Marie Curie) Damien Stehle École Normale Supérieure de Lyon Thomas Sturm University of Cantabria Bernd Sturmfels University of California, Berkeley Ashish Tiwari SRI International Jan Verschelde University of Illinois at Chicago Charles Wampler General Motors Research and Development Center Zhengfeng Yang Shanghai Key Lab of Trustworthy Computing Lihong Zhi Academy of Mathematics and System Sciences Officially Registered Participant Information Participants 46

Gender 46 Male 69.57% 32 Female 13.04% 6 Declined to state 17.39% 8

Ethnicity* 46 White 60.87% 28 Asian 13.04% 6 Hispanic 0.00% 0 Pacific Islander 0.00% 0 Black 2.17% 1 Native American 0.00% 0 Declined to state 23.91% 11 * ethnicity specifications are not exclusive Workshop on Mathematics Journals, February 14 - 16, 2011

Workshop on Mathematics Journals February 14, 2011 to February 16, 2011 MSRI, Berkeley, CA, USA

Organizers: James M Crowley (Society for Industrial and Applied Mathematics) Susan Hezlet* (London Mathematical Society) Robion C Kirby (University of California, Berkeley) Donald E McClure (American Mathematical Society)

Sponsors: Society for Industrial and Applied Mathematics London Mathematical Society American Mathematical Society Mathematical Sciences Publishers

Page 1 of 13 Workshop on Mathematics Journals, February 14 - 16, 2011

Mathematics journals: what is valued and what may change. Report of the workshop held at MSRI, Berkeley, California on February 14 – 16 2011

Mathematics relies on its journal literature as the main conduit for peer review and dissemination of research, and it does so more heavily and differently than other scientific fields. The conflict between universal access and the traditional subscription model that funds the journals has been debated for the past decade, while hard data on financial sustainability and usage under the different models has been slow to appear. However, the last ten years have seen the move from print to the electronic version of journals becoming the version of record, and the workshop took an evidence-based approach to discussing dissemination, access and usage of mathematics journals.

The workshop goal was to discuss what is important and unique to the publishing of mathematical research articles and how we can best ensure that publishing practices support peer reviewed research in the long term. Much of the current discussion is taking place between funders and publishers, including scholarly societies, but not directly with mathematicians. A second goal was to see if we can find a consensus of opinion on what is important about journal publishing to mathematicians, that is, where the balance lies between the need for profits from publishing and the desire for broader dissemination of research.

The presentations ranged widely; written reports of the talks make up the body of this document. During the first morning John Vaughn, Sam Rankin and Jim Crowley described the way the world works in Washington, leading us to think about the future of mathematics journals should new legislation be passed to mandate open access1 of federally sponsored research in the USA. Interleaved with those talks we had a presentation on the work of the IMU from John Ball and a talk from Jean Pierre Bourguignon that placed journals in the broader context of the research they publish and the work of a mathematician.

We heard talks on how mathematics journals work in practice and saw evidence of the growth of journals and the changing behaviour of readers and authors. Information was provided on the balance between not-for-profit and commercial publishers; the governance of learned societies; who reads mathematics journals; and the value of the older material to current mathematics research from the citation records. An unscheduled talk by Kristine Fowler, a librarian from the University of Minnesota gave some very interesting results from a recent survey of mathematicians’ views on open access. David Gabai’s talk on the recent history of the Annals of Mathematics provided a fascinating insight to the effect of free open access on the journal’s subscriptions, along with a description of the low cost of publishing the journal. Talks were presented by a variety of major mathematics publishers, ranging from the AMS and Elsevier to Project Euclid. Finally, new publishing models for changing access were presented from a variety of speakers: mathematicians, publishers and a new university office of scholarly communication.

Here is a summary of what we learned from the meeting.

Characteristics that distinguish mathematics journals from other disciplines: - there are lots of journals in the mathematical sciences – 774 listed ‘cover-to- cover’ in the Mathematical Reviews database alone; - they are fully international; one cannot distinguish how a journal operates according to which country it comes from; there are no boundaries to submission

1 ‘Open access’ refers to any research paper that is made freely available in published form at no cost to the reader; it does not distinguish between funded (gold) and unfunded (green) open access.

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from overseas authors and no boundaries to the choice of country where an author may submit a paper; - there are no speed pressures; refereeing is expected to be rigorous and detailed. The average time a paper spends between submission and acceptance is many months; - published articles form the building blocks of future mathematical research. A proof, once proved, stands for all time and is cited for as long as the literature can be found, it is therefore important not to lose the building blocks; - evidence was shown for the longevity of mathematics papers in terms of both continued reading and citation of the oldest material; - the community calls them referees rather than reviewers; journals frequently rely on a single referee to provide a rigorous check of the work, plus opinions from others on the relative importance of the work; - data sets and other supplemental materials are rare in pure mathematics and the paper stands on its own – this means there is no easy way to cheat in terms of the result presented, apart from direct plagiarism; - applied mathematics may include data and other supplemental material, but the data sets are commonly available and it is not a part of the culture to refuse to give background data; applied mathematics is distinct from applications of mathematics – both are valid but the relevance of the work is judged on different criteria.

On the arXiv: Mathematicians recognize the value of having free access to pre-refereed material and the presence of a preprint on the arXiv (http://arxiv.org/) already fulfils most of the requirements laid out by the green open access lobby. In view of the long referee times, posting a paper on the arXiv first establishes primacy of the result in the few cases where this is important to mathematicians. Publishers have learned that they cannot put the genies back in the bottles and that much of ‘their’ content is already freely available. Instead they work to promote the final published version as the ‘version of record’ and distinguish that from the arXiv version. Nowadays publishers encourage authors to post the early versions up to and including the final accepted version with a piece of acknowledgement ‘to be published in the Journal of X’. However many authors fail to keep the record updated and there are problems with referencing an arXiv preprint. This keeps the publishers happy that they still have something of value in hosting and selling the final published version in return for the costs of editing and dissemination.

For some sampled mathematics journals, as many as half the published papers have preprint versions posted on the arXiv and the percentage is growing. This makes the arXiv by far the dominant preprint repository and it is the first place many mathematicians in certain areas of the discipline look for new research. It is supported by the many thousands who choose to post their preprints there; no university or publisher forces them to do this. As a result there is very little enthusiasm in the mathematics community for alternative institutional repositories which are viewed as self-aggrandising university projects. The prior assertion of copyright ownership made by some universities in order to deposit articles in their own repositories has the effect of removing the right of the author to decide where they wish their work to be published. In contrast, the arXiv is widely and increasingly used; it is fully international and the barriers to posting an initial preprint are very low.

A problem is that there is no long term economic model for paying for the arXiv beyond the recent plea to major universities to support it through donations. We believe that there is an urgent need for the mathematics community to come up with a truly international solution during the next few years and it is hoped that researchers from other subject areas, most notably the theoretical physicists, are also looking for a solution. The arXiv may need a fully

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capitalized perpetual fund to be set up; the IMU might consider what it can do to facilitate further discussion.

On the archive: The switch to online versions as the primary source of mathematics journals has led to an interesting dilemma. Libraries would like to be the permanent repositories of the mathematical literature but have already begun to reduce their paper archives while not taking on the direct hosting of the journals they buy. The publishers are now responsible for archiving and upgrading the online versions in line with demand for more functionality. The question is what happens if the publisher folds? In the past the literature was scattered across many libraries. Nowadays publishers sign up to archiving services like CLOCKSS but this doesn’t meet the desire for upgrades, and storing out-of-date formats has little value. This is particularly important in mathematics where the rendering of mathematical symbols and formulas remains an issue. The recent development of MathJax is likely to help but may herald another change in format that will require publishers to charge for future developments. Libraries may need to review their long-term archiving policies.

Open access, green and gold:2 Mathematicians do not like the ‘gold’ open access model although Research Councils around the world are considering whether to fund mandated open access. There was general consensus that this model discriminates against unfunded authors, including retired authors and those from developing countries. The question was raised whether mathematicians should become involved in the judgement of ‘who pays’ for those papers where the author has no funding. It would be one more burden on mathematicians to identify the deserving needy but if they are not involved the publishers will make their own choices. If the NSF decides to fund a government-mandated open access policy, the money will go to those publishers who have set up charges for optional open access. For ‘gold’ open access, there is no embargo period and once the NSF has paid the fee, the article is immediately freely available online.

Evidence from the Annals experiment in ‘green’ open access was stark; libraries cancelled 34% of the subscriptions between 2003 and 2008 when the journal was freely available online. The Annals is one of the very best journals in mathematics and one of the cheapest journals; and so it came as a surprise to many at the workshop to hear that some of the best- funded libraries in the US had decided to save on the subscription rather than support the experiment in widening access.

On embargo periods: We did not hear anyone at the workshop support the principle of ‘green’ open access after a short embargo like the NIH model – a 12 month embargo period (i.e. a manuscript must be deposited by an author in a public access repository within 12 months of publication). Many mathematicians voluntarily post their preprints in the arXiv and this could answer the demand, if there is any, for public access. The window between a preprint being freely available on the arXiv, then again being freely available in published form just twelve months later is generally held to be too small given the long life of articles and the slow pace of publication in mathematics. The fear is that libraries will do as they did with the Annals, and cancel the journal subscriptions and have their readers look at the preprint version for an extra 12 months. With no subscription income and no ‘gold’ open

2 ‘green’ is free open access where nobody has paid but the article is made freely available; ‘gold’ is where someone, nominally the author but usually the research funder, pays to have the paper made freely available.

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access fees, many journals will not survive. However there was appreciable support for mandating green open access after a period that is more appropriate to mathematics, say after five years. This was mirrored by proposals from French and German mathematicians for making the archives of all journals freely available after five years. Should mathematicians be forced to choose a model for publicly funded future research, we think it likely that they would see five years as the best alternative even if it were at the expense of the closure of the very few ‘reverse’ moving wall experiments, such as those operated by the London Mathematical Society.

Other matters: Plagiarism, impact factors There was strong criticism of the misuse of journal impact factors to evaluate individual papers but concern was raised that it may not be possible for the IMU to provide any useful alternative index. Other concerns about the use of such metrics for quantifying journal quality have been well documented.

There was also a discussion on the apparent increase in plagiarism and in multiple submissions (where an author submits a paper to more than one journal simultaneously), along with the global rise in the number of mathematics papers being written. It was agreed that there is a need for societies/publishers to maintain standards. Tools such as CrossCheck have helped combat egregious cases, but these place an additional burden on staff and editorial boards. The arXiv is used by some Editors when checking complaints and there was a discussion on whether its use could be extended to provide a more formal registration of papers.

Conclusions The mathematics research community values its own standards of rigorous peer review, which they call refereeing, and the longevity of its journals. They want access to the old material and the certainty that it be maintained and remain accessible regardless of the medium. Mathematicians are wary of attempts to change scholarly publishing from a non- scientific political world that does not understand the value and nature of the mathematical literature.

Many people would like to change the funding model for mathematics journals, arguing that they wish to provide public access to publicly funded knowledge. The arXiv already provides public access but it suffers from having no long-term funding mechanism; we believe the most benefit to the community would come from addressing this problem and providing a permanent solution.

There is an argument for letting mathematicians decide what they want to support voluntarily rather than forcing new business models into the market. We should certainly encourage new experimental models, some of which have been very successful. Even those that are no longer free have helped put pressure to keep the price of journals down. Through allowing mathematicians to decide which model they want to support voluntarily, one can discover sustainable long term solutions. There may need to be some fail-safe mechanism to ensure that the past volumes of failed experimental journals are not lost to the literature.

The mathematics community has long argued against the high price of certain journals and would be happy to see a change in the funding model that reduces those profits that are not fed back into the research economy. As a result, the community is not closed to the idea of freeing up access, but it recognizes that any new model should not risk the long-term future of scholarly mathematics journals by imposing dangerously short mandated embargo periods. What the US government decides to do will affect the world-wide mathematics community. It

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is hoped that the US government does not force a model on its own researchers that may restrict the choice of where to submit a paper. There should also be a clear division between funding research and being involved in evaluating the output of the research once funded. Paying for publication may influence the reader’s judgement of the value of the research. In general, we see such schemes as unfair and a barrier to new research from unfunded mathematicians. If mandated open access were to be funded, there would be a case for no embargo period. Many publishers have already set up optional paid open access schemes to accommodate research funders who may impose a mandate. It is to be hoped that ‘green’ open access would not be imposed that mandates open access twelve months after publication; five years is considered a more appropriate period for mathematics.

Disclaimer We have written the conclusions in the knowledge that it will never be possible to find a perfect list and certainly not all the workshop participants would support these views which are our own. However, we believe it important to assert the unique value of peer-review in mathematics journals and to describe what is necessary to support a healthy structure in which the very best of mathematical research can be distinguished while maintaining the breadth of mathematics journals. The many diverse journals in the mathematical sciences provide a platform for worthy research which has real value. We hope that this report may be used in future debates as fuel for the phrase ‘one size does not fit all’.

James Crowley SIAM, Susan Hezlet LMS, Robion Kirby Berkeley, Don McClure AMS.

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Invited Speakers First Name Last Name Current Institution John Ball University of Oxford Jean-Pierre Bourguignon École Polytechnique David Clark Elsevier Science James Crowley SIAM - Society of Industrial and Applied Mathematics David Gabai Princeton University Robert Guralnick University of Southern California Susan Hezlet London Mathematical Society Carol Hutchins New York University, Courant Institute Robion Kirby University of California, Berkeley Hans Koelsch Springer, Science, Technology, Medicine Matthias Kreck Hausdorff Research Institute, University of Bonn A. Macintyre Queen Mary, University of London Paolo Mangiafico Duke University Donald McClure American Mathematical Society Samuel Rankin American Mathematical Society Bernard Teissier Centre National de la Recherche Scient John Vaughn Association of American Universities Mira Waller Duke University Press Thomas Ward University of East Anglia

Page 7 of 13 Workshop on Mathematics Journals, February 14 - 16, 2011

Schedule

Monday, February 14, 2011 9:00AM - 9:20AM Simons Auditorium Welcome Introduction - Why are we here and what do we 9:20AM - 9:30AM Simons Auditorium Susan Hezlet hope to get out of this? John Vaughn | Expanding Public Access to Research Results: Finding a 9:30AM - 9:50AM Simons Auditorium Common Path Forward The Work of IMU and CEIC on Journals and 9:50AM - 10:10AM Simons Auditorium John Ball Related Issues 10:10AM - 10:40AM Tea 10:40AM - 11:00AM Simons Auditorium Samuel Rankin Policymakers and Open Access Jean-Pierre 11:00AM - 11:20AM Simons Auditorium TBA Bourguignon The Manifold Atlas Project - a Model for Future 11:20AM - 11:40AM Simons Auditorium Matthias Kreck Publishing? 11:40AM - 12:10PM Simons Auditorium Panel Discussion 12:10PM - 1:40PM Lunch 1:40PM - 1:45PM Simons Auditorium Donald McClure Introduction to Session 2 Report by participants on conversations with the National Science 1:45PM - 2:05PM Simons Auditorium Foundation, the National Science Board and the Office of Science and Technology Policy Avenues for Mathematics Journals - on the road to 2:05PM - 2:25PM Simons Auditorium Hans Koelsch 2025 Everything you did before (and more!) but with a 2:25PM - 2:45PM Simons Auditorium James Crowley new financial model 2:45PM - 3:00PM Simons Auditorium Panel Discussion 3:00PM - 3:30PM Tea 3:30PM - 4:15PM Simons Auditorium Breakout Groups 4:15PM - 5:00PM Simons Auditorium Reporting Back and Wrap-Up Discussion Tuesday, February 15, 2011 9:00AM - 9:10AM Simons Auditorium Robion Kirby Introduction to Session 3 9:10AM - 9:30AM Simons Auditorium Donald McClure Summary of Results of Day 1 Remarks on the "Ecology" of Mathematical 9:30AM - 9:50AM Simons Auditorium Carol Hutchins Journals 9:50AM - 10:10AM Simons Auditorium A. Macintyre The View from a Learned Society Dynamics of Mathematics Journals from 2000 to 10:10AM - 10:30AM Simons Auditorium Donald McClure 2009 10:30AM - 11:00AM Tea Access and Dissemination of Mathematics 11:00AM - 11:20AM Simons Auditorium David Clark Journals: A Commercial Publisher's Perspective Paolo Mangiafico | On the Exchange of Apples and Ideas: A Brief 11:20AM - 11:40AM Simons Auditorium Overview of Emerging Models for Scholarly Communication 11:40AM - 12:10PM Simons Auditorium Panel Discussion 12:10PM - 1:40PM Lunch 1:40PM - 1:45PM Simons Auditorium James Crowley Introduction to Session 4 1:45PM - 2:05PM Simons Auditorium Bernard Teissier A Charter for Sustainable Publishing

Page 8 of 13 Workshop on Mathematics Journals, February 14 - 16, 2011

An Editor's view of recent challenges faced by the 2:05PM - 2:25PM Simons Auditorium David Gabai Annals 2:25PM - 2:45PM Simons Auditorium Susan Hezlet Mathematics journals: who reads them? 2:45PM - 3:00PM Simons Auditorium Panel Discussion 3:00PM - 3:30PM Tea 3:30PM - 4:15PM Simons Auditorium Breakout Groups 4:15PM - 5:00PM Simons Auditorium Reporting Back and Wrap-Up Discussion 5:00PM - 6:00PM Reception Wednesday, February 16, 2011 9:00AM - 9:10AM Simons Auditorium Susan Hezlet Introduction to Session 5 9:10AM - 9:30AM Simons Auditorium James Crowley Summary of Results of Day 2 9:30AM - 9:50AM Simons Auditorium Tom Ward | The mill(in)er\\'s tale The Economics of Math Journals Supported by 9:50AM - 10:10AM Simons Auditorium Robion Kirby Page Charges 10:10AM - 10:30AM Simons Auditorium Robert Guralnick Random Thoughts on Mathematical Journals 10:30AM - 11:00AM Tea Mira Waller | Nonprofit Publishing: Juggling Resources and Balancing 11:00AM - 11:20AM Simons Auditorium Conflicting Needs 11:20AM - 11:50AM Simons Auditorium Panel Discussion 11:50AM - 12:20PM Simons Auditorium Breakout Groups 12:20PM - 1:00PM Simons Auditorium Reporting Back and Wrap-Up Discussion 1:00PM - 2:30PM Lunch

Page 9 of 13 Workshop on Mathematics Journals, February 14 - 16, 2011

Officially Registered Participants First Name Last Name Current Institution John Ball University of Oxford Jean-Pierre Bourguignon École Polytechnique Robert Bryant University of California, Berkeley Jeffra Bussmann University of California, Irvine David Clark Elsevier Science Anita Colby University of California, Berkeley James Crowley SIAM - Society of Industrial and Applied Mathematics Paulo de Souza University of California, Berkeley John Ewing Math for America Kristine Fowler University of Minnesota Twin Cities David Gabai Princeton University Bruce Garrod University of Toronto Sergei Gelfand American Mathematical Society Daniel Goroff Alfred P. Sloan Foundation Joseph Grcar Sandia National Laboratory Robert Guralnick University of Southern California Aloysius Helminck North Carolina State University Bob Heyer-Gray University of California, Davis Susan Hezlet London Mathematical Society Jane Holmquist Princeton University Carol Hutchins New York University, Courant Institute Arne Jensen University of California, Berkeley Nicholas Jewell University of California, Berkeley Deborah Kegel University of California, San Diego Robion Kirby University of California, Berkeley Hans Koelsch Springer, Science, Technology, Medicine Robert Korsan University of Pittsburgh Steven Krantz Washington University Matthias Kreck Hausdorff Research Institute, University of Bonn Darla Kremer National Science Foundation Keonhee Lee Chungnam National University A. Macintyre Queen Mary, University of London Paolo Mangiafico Duke University

Page 10 of 13 Workshop on Mathematics Journals, February 14 - 16, 2011

Officially Registered Participants First Name Last Name Current Institution Donald McClure American Mathematical Society Nadia Michalak Mathematical Sciences Publishers Fatemeh Mohammadi Mathematical Sciences Research Institute Maria Oliveira American Mathematical Society Ann Perbohner Dartmouth College Ivars Peterson MAA - Mathematical Association of America Markus Pflaum University of Colorado Jim Pitman University of California, Berkeley George Porter California Institute of Technology Brian Quigley University of California, Berkeley Samuel Rankin American Mathematical Society Kenneth Ribet University of California, Berkeley Linda Riewe MSRI - Mathematical Sciences Research Institute Karl Rubin MSRI - Mathematical Sciences Research Institute Maureen Schupsky Princeton University Alexandru Scorpan Mathematical Sciences Publishers Ev Shafrir Mathematical Sciences Publishers Alice Silverberg University of California, Berkeley Erich Staib Duke University Press Bernard Teissier Centre National de la Recherche Scient Martha Tucker University of Washington John Tuley University of Colorado John Vaughn Association of American Universities Ivonne Vetter Mathematical Association of America Mira Waller Duke University Press Thomas Ward University of East Anglia Ron Wasserstein American Statistical Association Carol Wood Wesleyan University Linda Yamamoto Stanford University

Page 11 of 13 Workshop on Mathematics Journals, February 14 - 16, 2011

Officially Registered Participant Information Participants 62

Gender 62 Male 54.84% 34 Female 32.26% 20 Declined to state 12.90% 8

Ethnicity* 62 White 67.74% 42 Asian 8.06% 5 Hispanic 3.23% 2 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 20.97% 13 * ethnicity specifications are not exclusive

Page 12 of 13

Circle on the Road Spring 2011 March 18, 2011 to March 20, 2011 University of Houston, Houston, TX, USA

Organizers: David Auckly (Mathematical Sciences Research Institute) Matthias Kawski (Arizona State University) Jeff Morgan (University of Houston) Mark Saul (National Science Foundation) Sam Vandervelde (St. Lawrence University) 2011 Circle on the Road Report

The 2011 Circle on the Road workshop was the second workshop in this series. These Circle on the Road workshops take place in communities that are either not served or are under-served by mathematical outreach programs. These workshops bring together people who wish to start a math circle together with experienced math circle leaders. The first and third days of the workshop consist of presentations, panel discussions and small group discussions. The second day of the workshop features a mathematics festival in the community. This festival attracts more than 250 students to spend the day exploring mathematics. Teams of mathematicians run the festival. Each team includes several apprentices who will be learning how to teach a math circle lesson from the team leader, who is an experienced math circle leader. At the festival, the apprentices first watch the expert and later take over activities. The direct mentoring of apprentices by experienced leaders is one of the most important elements of these workshops. Having instructors apprentice under expert instructors and receive feedback on their presentations is as powerful as it is rare. It is also important to note that the groups evaluate and refine the math circle activities developed for the festival during the third day of the workshop. The 2011 workshop took place at the University of Houston. The overall structure of this workshop was similar to the structure of the 2010 workshop. We did make a few adjustments to improve the workshop based on what we learned from the first workshop. We ran the mathematics festival on the second day of the workshop. See the festival poster on the next page. We did not have self-guided activities available at the same time as the sample math circle sessions. We also used the wiki capabilities of the NAMC website to capture the planning of the math circle sessions. We feel that the view of the planning process, together with the finished hand-outs, lesson plans and session video combine together to create a unique resource for people interested in learning how to run a math circle. One highlight of this workshop was the mathematical construction of Vi Hart, and her presentation on mathematical projects. Vi is well known for her Mathematical Doodling videos http://vihart.com/doodling/. Prior to this workshop she was unaware of the math circle movement. Now she is an avid supporter of the movement. Her materials are also very useful for math circles. Another interesting thing about the math festival is that it was interrupted by a fire alarm in the building. Rather than stopping the festival, this just added new life to the festival. Everyone exited the building, and then the experienced math circle leaders started spontaneous mathematical demonstrations that could be done outside without paper or chalkboards. It was a very good demonstration of the depth, variety, and flexibility of methods used in the math circle model. More than 110 mathematicians attend the 2011 circle on the Road workshop. The Evaluation summary is attached as an appendix. Each Circle on the Road Workshop generates a dozen new math circle lessons that are added to the website with video and commentary. Each one also attracts about a dozen teams of who go out and start new math circles after the workshop.

Screen shot of a lesson plan page with embedded video from the 2010 CoR

We have established a strong relationship with the Special Interest Group of the Mathematical Association of America on Math Circles for Students and Teachers (SIGMAA-MCST). We work together to organize sessions at MathFest, the annual conference of the MAA, and at the Joint Meetings of the AMS and MAA. At MathFest, we host a booth in the exhibit area that serves as a meeting place and information exchange for people involved in math circles, a central location to distribute the schedule of events relevant to math circles at the conference, as well as disseminating information about circles to potential new circle leaders.

The workshop is an integral part of our efforts to spread the math circle movement across the US. Combined with our website, and our math circle grants, our efforts have proven effective. There were only 20 US math circles in 2009. In the Fall of 2010 there were 80. Byu December 2011 there were 124 registered circles, and the movement is growing faster than originally thought possible.

Map of North American Math Circles December, 2011

Participants First Name Last Name Institute Maria Acosta Ashley Ahlin Lorna Almocera Titu Andreescu Skona Brittain Julia Brodsky Marie Brodsky gloria BrownBrooks Santa Ana Opportunity School Anna Burago Silva Chang Jocelyn Comstock Katherine Cook David Cordeiro Judith Covington Craig Daniels Sergey Dankin Nasser Dastrange Maria AIlynn Diansuy Maria Droujkova Marta Eso Daniel Finkel Sangeeta Gad Shanzhen Gao Florida Atlantic University Leszek Gawarecki Claire Geistfeld Vinton Geistfeld Sergey Genkin Linda Goertz Linda Green James Hall Michael Hall University of California David Hankin Brooklyn College, CUNY Vi Hart Neil Hoffman University of Texas Pat Jones University of Louisiana--Lafayette Matthias Kawski Arizona State University Edward Keppelmann University of Nevada In-Jae Kim Joanne Kimball Sherman Melrose Public Schools Nadya Kiuger Emily Landes Jonathan Li Ina Loobeek Andrew Ma Tingting Ma Texas A & M University Xuan Ma Catherine McKay Wollinsky Mendez Martin Montgomery christian mukeba Michael Nakamaye University of New Mexico jean paul ngoma Matthew O'Toole Mary OKeeffe Albany Area Math Circle' Katharine Ott University of Kentucky Nina Otterson Elizabeth Parizh Ming Jack Po Shira Polster Olga Radko University of California Harold Reiter University of North Carolina Mitra Roehr Tim Sanders mathleague.org Mark Saul New York University, Courant Institute Amanda Serenevy Tatiana Shubin Sara Smithback Stacia Taylor Daniel Ullman George Washington University Sara Vale Sam Vandervelde St. Lawrence University Monika Vo Ruilin Wang Diana White Brandy Wiegers MSRI - Mathematical Sciences Research Institute Lee Windsperger Louisiana State University Japheth Wood Bard College Philip Yasskin Texas A & M University Alex Zivkovic Joshua Zucker Officially Registered Participant Information

Participants 80

Gender 80 Male 43.75% 35 Female 56.25% 45 Declined to state 0.00% 0

Ethnicity* 80 White 70.00% 56 Asian 17.50% 14 Hispanic 3.75% 3 Pacific Islander 0.00% 0 Black 1.25% 1 Native American 1.25% 1 Mixed 1.25% 1 Declined to state 5.00% 4 * ethnicity specifications are not exclusive Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

responses

Summary See complete responses

How many years have you been involved in Math Circles? Just getting started 15 26% Started this year 10 18% 1-2 years 10 18% 3-5 years 8 14% 5-10 years 8 14% 10-15 years 3 5% 15+ years 1 2% All of my life 2 4%

What types of Math Circles are you involved in? Student (elementary) 16 29% Student (middle school) 34 61% Student (high school) 31 55% Teacher 20 36% None - I'm looking forward to starting one soon! 3 5% Parent 5 9% Other 5 9%

People may select more than one checkbox, so percentages may add up to more than 100%.

What is/ Will be your Math Circle role? Math Circle Instructor 43 77% Math Circle Director 26 46% Math Circle Founding Director 30 54% Grant Writer 14 25% Parent 8 14% None - I'm looking forward to being involved later 2 4% Other 5 9%

People may select more than one checkbox, so percentages may add up to more than 100%.

Have you attended previous Math Circle events?

1 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

None prior to Circle on the Road 1998 MSRI Workshop: Conversation between Mathematics Teachers and Mathematics Researchers:The Bay Area Mathematical Olympiad 2004 MSRI Workshop: Mathematical Circles and Olympiads 2007 Math Circle Special Session - JMM (New Orleans) 2008 NAMC Reception - JMM (San Diego) 2009 NAMC Reception - JMM (DC) 2009: MSRI Great Circles Workshop 2009 Math Fest SIGMAA MCST Special Session (Portland) 2010 JMM SIGMAA MCST Special Session (San Francisco) 2010 Circle on the Road (Arizona) 2010 Math Fest SIGMAA MCST Special Session (Pitsburgh) 2011 JMM SIGMAA MCST Special Session (New Orleans) Other

People may select more than one checkbox, so percentages may add up to more than 100%.

Your Math Circle Experience

Please describe the Circle on the Road 2011 Workshop in 2 sentances. It was an eye-opening experience. Kids came with their parents and/or teachers to the sessions. All of them were eager to learn, and having fun by working on math problems. This is something that I'd like to see in my town. For someone working without colleagues, in a relatively small town, this was an outstanding opportunity to meet a huge variety of highly experienced people and learn about a wide range of resources, to see others at work, to work together with others to refine math circle sessions, and to introduce many Houston kids to some engaging mathematics. (Sorry, that's one run on ...

Please describe 1 or 2 things that you gained by attending the workshop. Serving as an apprentice for a session was a great experience. The leader of the group has lots of experiences of working with kids, and the lesson plan was well prepared. I learned a lot by working with the leader and students (and their parents). I'm just getting started, so to meet so many people with a vast amount of experience was like opening a treasure chest. We were also able to form a small network of those working with elementary circles, so we can continue to communicate and help one another with ideas, as well as helping those who are interested in starting. Working with other m ...

What is a Math Circle? It is a fun social forum where people can enjoy doing mathematics. An opportunity for interested students to explore mathematics outside the traditional curriculum in an engaging way, with peers, led by those with mathematical depth. In my opinion, they share the following common traits: *focus on motivating and exciting the students about math * using heuristic and adaptive approach to guide the learning process * Student-oriented learning process allows the students to build confidence through exploration and fellowship A math circle is a gathering of individuals all interested in and excit ...

Follow-up Resources

How useful did you find the Overall Circle on the Road Workshop? - Very Useul 36 63% Useful 10 18% Somewhat Useful 3 5% Not Useful 0 0%

Which topics were the most useful for you from the workshop Sessions - Compare and Contrast Math Circles (panel) Very Useful 20 35% Useful 19 33% Slightly Useful 7 12% Not Useful at All 0 0% N/A - Wasn't Present 9 16%

2 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Which topics were the most useful for you from the workshop Sessions - Sample Math Circle Session: Chromatic Numbers and More (Tatiana Shubin) Very Useful 27 47% Useful 17 30% Slightly Useful 5 9% Not Useful at All 0 0% N/A - Wasn't Present 6 11%

Which topics were the most useful for you from the workshop Sessions - Session Planning Very Useful 21 37% Useful 24 42% Slightly Useful 5 9% Not Useful at All 0 0% N/A - Wasn't Present 7 12%

Which topics were the most useful for you from the workshop Sessions - Banquet Very Useful 20 35% Useful 25 44% Slightly Useful 8 14% Not Useful at All 0 0% N/A - Wasn't Present 4 7%

Which topics were the most useful for you from the workshop Sessions - Gamification and Alternate Reality Games (Maria Droujkova) Very Useful 11 19% Useful 13 23% Slightly Useful 17 30% Not Useful at All 5 9% N/A - Wasn't Present 10 18%

Which topics were the most useful for you from the workshop Sessions - Math Clubs and Their Social Aspect: A View Inside and Out (Elizabeth Parizh) Very Useful 16 28% Useful 15 26% Slightly Useful 16 28% Not Useful at All 2 4% N/A - Wasn't Present 7 12%

Which topics were the most useful for you from the workshop Sessions - How Can (or Should) Math Circles be Tied to the Curriculum? (panel)

3 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Very Useful 24 42% Useful 13 23% Slightly Useful 14 25% Not Useful at All 3 5% N/A - Wasn't Present 3 5%

Which topics were the most useful for you from the workshop Sessions - My Favorite Workshops (Vi Hart) Very Useful 26 46% Useful 20 35% Slightly Useful 7 12% Not Useful at All 2 4% N/A - Wasn't Present 2 4%

Which topics were the most useful for you from the workshop Sessions - Good Activities for Math Circles (panel) Very Useful 25 44% Useful 17 30% Slightly Useful 7 12% Not Useful at All 0 0% N/A - Wasn't Present 6 11%

Which topics were the most useful for you from the workshop Sessions - The Orange County Math Circle - A *student organized* circle (Jonathan Li, Alex Zivkovic, Andrew Ma) Very Useful 25 44% Useful 6 11% Slightly Useful 9 16% Not Useful at All 1 2% N/A - Wasn't Present 16 28%

Which topics were the most useful for you from the workshop Sessions - Evaluation Focus Groups Very Useful 11 19% Useful 11 19% Slightly Useful 10 18% Not Useful at All 4 7% N/A - Wasn't Present 20 35%

Which topics were the most useful for you from the workshop Sessions - Always Be Prepared (Brandy Wiegers)

4 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Very Useful 16 28% Useful 10 18% Slightly Useful 6 11% Not Useful at All 2 4% N/A - Wasn't Present 21 37%

Please share any comments related to your rankings above for the workshop Program Seeing what other people's work and idea is always great leading me to the next level of session preparation and greater motivation, since their work and idea usually come with their love and philosophy on mathematics in general. Maybe we could have had a variety of "circle presentations" on Friday so participants could choose what was most relevant for them. I spoke with Andrew Ma outside the workshop and found their Math Circle to be unique and dynamic. HOpe soon we can expand their model to other circles. As a new leader of a Math TEACHERS' Circle, I wish there had been more time to discu ...

Which topics were the most useful for you from Saturday's Sessions - Puzzle area Very Useful 8 14% Useful 9 16% Slightly Useful 3 5% Not Useful at All 0 0% N/A - Wasn't Present 29 51%

Which topics were the most useful for you from Saturday's Sessions - Pile Splitting Very Useful 8 14% Useful 4 7% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 38 67%

Which topics were the most useful for you from Saturday's Sessions - Multiplication Graphs Very Useful 12 21% Useful 4 7% Slightly Useful 0 0% Not Useful at All 0 0% N/A - Wasn't Present 35 61%

Which topics were the most useful for you from Saturday's Sessions - Circles of Differences Very Useful 7 12% Useful 5 9% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 38 67%

Which topics were the most useful for you from Saturday's Sessions - Regions of a Circle and Difference Equations

5 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Very Useful 2 4% Useful 5 9% Slightly Useful 0 0% Not Useful at All 0 0% N/A - Wasn't Present 43 75%

Which topics were the most useful for you from Saturday's Sessions - Any Conic Section Very Useful 3 5% Useful 5 9% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 39 68%

Which topics were the most useful for you from Saturday's Sessions - The Great Popcorn Prank Very Useful 5 9% Useful 4 7% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 39 68%

Which topics were the most useful for you from Saturday's Sessions - Playing with Parity Very Useful 9 16% Useful 6 11% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 35 61%

Which topics were the most useful for you from Saturday's Sessions - The Game of Nim Very Useful 8 14% Useful 5 9% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 37 65%

Which topics were the most useful for you from Saturday's Sessions - Origami Very Useful 12 21% Useful 5 9% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 33 58%

6 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Which topics were the most useful for you from Saturday's Sessions - KenKen Very Useful 11 19% Useful 1 2% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 37 65%

Which topics were the most useful for you from Saturday's Sessions - Pythagorean Fractal Auctions Very Useful 10 18% Useful 4 7% Slightly Useful 0 0% Not Useful at All 0 0% N/A - Wasn't Present 37 65%

Which topics were the most useful for you from Saturday's Sessions - Tiling and Induction Very Useful 9 16% Useful 3 5% Slightly Useful 0 0% Not Useful at All 0 0% N/A - Wasn't Present 37 65%

Which topics were the most useful for you from Saturday's Sessions - Map Coloring Very Useful 10 18% Useful 3 5% Slightly Useful 1 2% Not Useful at All 0 0% N/A - Wasn't Present 35 61%

Which topics were the most useful for you from Saturday's Sessions - Whisk Management: a mathematical construction project Very Useful 6 11% Useful 6 11% Slightly Useful 4 7% Not Useful at All 1 2% N/A - Wasn't Present 33 58%

Please share any comments related to your rankings above for Saturday's Program. I served as an apprentice of Dr. Harold Reiter who was running the KenKen session. It was a great pleasure to work with him, and I learned a lot from his well-organized and enthusiatic sessions. Since my time was totally dedicated to the KenKen session, I didn't have a chance to attend other sessions (No regret though). As an apprentice, I would have enjoyed seeing other programs, or even just hearing a few minute summary of the program and getting handouts, but I was in our own session all three times. Popcorn Prank is an excellent session. The leader shows not only her ability to instill mat ...

How often do you expect you will use the following resources: - People you met at Circle on the Road?

7 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Everyday 3 5% Once a Week 18 32% Once a Month 20 35% Every Once in a While 16 28% Never 0 0%

How often do you expect you will use the following resources: - Lesson plans for the sample circles (once posted)? Everyday 0 0% Once a Week 16 28% Once a Month 31 54% Every Once in a While 10 18% Never 0 0%

How often do you expect you will use the following resources: - Videos from workshop presentations (once posted)? Everyday 0 0% Once a Week 7 12% Once a Month 17 30% Every Once in a While 29 51% Never 4 7%

How often do you expect you will use the following resources: - Sample circle videos from the festival (once posted)? Everyday 0 0% Once a Week 5 9% Once a Month 20 35% Every Once in a While 30 53% Never 1 2%

How often do you expect you will use the following resources: - MSRI Math Circle Library of Books? Everyday 0 0% Once a Week 15 26% Once a Month 21 37% Every Once in a While 16 28% Never 2 4%

How often do you expect you will use the following resources: - NAMC Website, http://mathcircles.org? Everyday 2 4% Once a Week 28 49% Once a Month 14 25% Every Once in a While 12 21% Never 0 0%

8 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Circle on the Road Organization

How did you hear about the Circle on the Road Workshop? Personal Invite from the Program Coordinators 43 75% Joint Math Meetings - SIGMMA Math Circles for Students and Teachers Special Session 9 16% NAMC website (http://mathcircles.org) 8 14% NAMC Newsletter 4 7% Other 13 23%

People may select more than one checkbox, so percentages may add up to more than 100%.

Please Rank the Following Workshop Aspects - Pre-Conference Publicity The Best Ever 4 7% Very Good 24 42% Acceptable 15 26% Unacceptable 2 4% N/A 11 19%

Please Rank the Following Workshop Aspects - Conference Registration The Best Ever 11 19% Very Good 36 63% Acceptable 8 14% Unacceptable 0 0% N/A 2 4%

Please Rank the Following Workshop Aspects - Pre-Conference Communication The Best Ever 15 26% Very Good 23 40% Acceptable 16 28% Unacceptable 1 2% N/A 1 2%

Please Rank the Following Workshop Aspects - Math Festival (Saturday) The Best Ever 16 28% Very Good 28 49% Acceptable 12 21% Unacceptable 0 0% N/A 1 2%

Please Rank the Following Workshop Aspects - Math Circle Debrief

9 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

The Best Ever 8 14% Very Good 24 42% Acceptable 10 18% Unacceptable 0 0% N/A 11 19%

10 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Please Rank the Following Workshop Aspects - Math Circle Professional Presenations The Best Ever 21 37% Very Good 26 46% Acceptable 5 9% Unacceptable 0 0% N/A 2 4%

Please Rank the Following Workshop Aspects - Banquet The Best Ever 6 11% Very Good 25 44% Acceptable 16 28% Unacceptable 3 5% N/A 7 12%

Please Rank the Following Workshop Aspects - Post-Conference Resources The Best Ever 8 14% Very Good 24 42% Acceptable 7 12% Unacceptable 0 0% N/A 17 30%

Please share any comments related to your rankings above. I am very impressed by the level of dedication by the MSRI organizers. They are just ready to do what pariticipants need. Super fantastic!! I think many of these sessions could have been geared at a wider age range, especially in different iterations. E.g., the tiling talk might have been done at the elementary level once, and at the middle/high school level twice. Given the high demand for elementary activities (relative to what was offered), this could help meet demand. It might also provide opportunities for those math circle leaders who find elementary hard (including myself) the chanc ...

Future Circle on the Road Workshops

Should we repeat this event in the future? YES 57 100% NO 0 0% Other 0 0%

People may select more than one checkbox, so percentages may add up to more than 100%.

Would you like to participate in a future Circle on the Road Workshop? YES 53 93% NO 1 2% Other 3 5%

People may select more than one checkbox, so percentages may add up to more than 100%.

11 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

Would you like to recommend to others that they participate in a future Circle on the Road Workshop? YES 54 95% NO 1 2% Other 2 4%

People may select more than one checkbox, so percentages may add up to more than 100%.

Where should we have a future NAMC Circle on the Road Workshop? Some place with mild temperature for spring workshop Some place close to ocean for summer workshop Some place in rocky mountain area for fall workshop Some place warm for winter workshop Indianapolis! Xuan Ma Somewhere in the Southeast or the East Coast - perhaps Washington, DC or Baltimore. Actual places don't come to mind, but clearly somewhere with nice weather and a large population. San Diego comes to mind first. Atlanta, Dallas The Bay Area seems to have a variety of math circle leaders. Saint Leo University or somewhere in Florida. I don't know enough to make any recommendation. However, ...

When should we have a future NAMC Circle on the Road Workshop January 13 25% February 17 33% March 37 71% April 27 52% May 16 31% June 18 35% July 17 33% August 15 29% September 12 23% October 19 37% November 18 35% December 10 19% Other 3 6%

People may select more than one checkbox, so percentages may add up to more than 100%.

Any comments about the timing of the event? Speaking personally, I don't do math/work on Sundays, so I would prefer a weekday workshop, terminating on Saturday, but I expect that's counter to most preferences. Comfortable weather. This event was during our Spring Break. It wasn't a big deal to attend it just involved more complicated travel plans. However, I think because it was also Spring Break in Texas, we did not get any undergraduate volunteers. I think their presence would have made Saturday's program even more exciting, so if possible I think the event should take place outside of Spring Break at least locally. I think the time ...

Thank you

Thank you for taking time to complete the 2010 Circle on the Road Conference Evaluation. We appreciate your feedback and look forward to using it to improve the future workshops!

If you are not a member of NAMC and would like to join, please enter your e-maill address below. [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] monika.vo

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This is the space to add any last comments that weren't covered in other places in the survey. Thank you for this great opportunity!! Awesome!! I would have enjoyed a session on developing elementary circles, but we did find each other and had ample chances to talk during unscheduled time. I would also have benefited from taking a few minutes at the beginning to have people briefly introduce themselves (name, location, type of circle). As it turned out, someone who lives 3 miles from me was also just starting a circle, and it was a huge benefit to meet, but we might have missed the chance had he not overheard me mention my state. (A directory might have served a similar purpose.) I was ...

12 of 13 4/25/2012 12:50 PM Edit form - [ Circle on the Road 2011 Evaluation ] - Google Docs https://docs.google.com/spreadsheet/gform?key=0AljaiXiPXvA-dG1n...

What is your name? In-Jae Kim Ashely Ahlin Xuan Ma Katharine Ott Judith Covington Alex Zivkovic Maria Acosta Leszek Gawarecki Moon Lee Shanzhen Gao Matthias Kawski Tingting Ma Ruilin Wang Monika Vo gloria Brown Brooks Sam Vanderveld ...

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Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers May 11, 2011 to May 13, 2011 MSRI, Berkeley, CA, USA

Organizers: Dave Auckly Sybilla Beckmann (chair) Jim Lewis and William McCallum MATHEMATICAL SCIENCES RESEARCH INSTITUTE Report on the 2011 Critical Issues in Mathematics Education Workshop “Mathematical Education of Teachers”

The eighth Critical Issues in Mathematics Education (CIME) workshop took place at MSRI May 11–13, 2011. This was the third workshop in this series addressing teacher training. The second workshop addressed the mathematical knowledge needed for teaching, and the fourth workshop emphasized teaching teachers mathematics. The adoption of the Common Core State Standards in Mathematics (CCSSM) implied that many practicing teachers would be given training to implement the new standards, and the ways in which pre-service teachers are trained would have to be adjusted to reflect the CCSSM. Thus the 2011 workshop addressing teacher training was very timely.

The 2011 workshop showcased successful teacher programs, discussed the Common Core State Standards, and explored how mathematics education research could improve practice. Sybilla Beckman kicked off the workshop with an introduction and a challenge to the mathematical education community. She pointed out that people in the mathematical research community share their research with each other and this research is recognized and appreciated by peers and colleagues. In comparison, much of what happens in classrooms is hidden, and it is difficult for peers and colleagues to learn from something that they do not see. She further suggested that lesson study may be a way to share what happens in classrooms.

The workshop had several different themes. The common core, and the opportunities that it represents for improving the mathematical education of teachers, was one theme. Some people also expressed concerns about the CCSSM, but overall participants thought the CCSSM represents a positive development, and that it would matter more how the education community implements the new standards.

Challenges represented a second theme. The biggest challenge with mathematics education is the scale of the endeavor. The conference addressed what needs to be changed in teachers’ mathematical education. A starting point was what pre-service teachers need to learn. In particular they should acquire mathematically rich content knowledge and specialized knowledge for teaching. It is important that children’s mathematical thinking is considered when this knowledge is identified. Just as the CCSSM provides a uniform framework for student instruction, Dr. Deborah Ball suggested that a common framework for training teachers be developed that incorporates methods by which they can address the Common Core requirements.

One of the most exciting themes of the workshop was the concept of lesson study. Dr. Catherine Lewis of Mills College gave an overview of lesson study, the process of looking closely at what others have done, trying to make improvements upon prior work, and bringing new ideas and insights to this work. Other professors described lesson study in various contexts: for pre-service teachers, school-wide, district-wide, in regions and even country-wide.

Dr. Raven McCrory of Michigan State University presented research on the effectiveness of current teacher training programs for elementary teachers. She used data from a study of over 2000 undergraduates at certifying institutions in four states. Maria Teresa Tatto, also of Michigan State

2 University, presented an international comparison of mathematics teacher education using data from approximately 24,000 future primary and secondary mathematics teachers in 17 countries.

Dr. Herbert Clemens of Ohio State University provided the closing summary. He pointed out that the acceptance by the States of the Common Core Mathematics Standards represents a once-in-a-lifetime opportunity for mathematics teachers to enhance their professional status much in the same way that university mathematicians did during the post-Second World War era. Mathematics teachers themselves will have to drive this process--numbers of teachers are too big, and the interests of other constituencies too compromised, for it to be otherwise. But the university community and the government, among others, can help in essential ways. Those include programs for teacher-leaders and teacher professional developers, and the nurturing of 'laboratories of excellence.'

A complete list of speakers, and the subjects they covered, is attached.

These comments from participants indicate the impact the workshop has on those attending: Leslie Sena wrote “I attended the CIME workshop in May. It was a wonderful way to connect with others in the profession.” Sandie Gilliam wrote “I look forward to the next CIME conference. They are well organized and I find them so applicable to my duties.” Heather Boles wrote “My colleague, Gail Johnston, attended the MSRI session in May which focused on Critical Issues in Mathematics Education. She returned to Iowa State University with new connections, insights, and resources as we discuss how we teach mathematics to future teachers. She spoke about how valuable the conference is/was.”

To make this information available to a larger audience, MSRI maintains a web page with links to descriptions of all eight workshops at www.msri.org/web/msri/static-pages/-/node/6. Included are slides and video from presentations, schedules, and lists of participants.

3 Invited Speakers First Name Last Name Current Institution Deborah Ball University of Michigan Sybilla Beckmann University of Georgia Richard Bisk Worcester State University Diane Briars National Council of Supervisors of Mathematics Herbert Clemens Ohio State University Jerry Dwyer Texas Tech University Robert Farinelli American Mathematical Association of Two-Year Joan Ferrini-Mundy National Science Foundation Astrid Fossum Milwaukee Public Schools David Foster Silicon Valley Mathematics Initiative E. Paul Goldenberg Center for Mathematics Education Melissa Hedges Mequon-Thiensville School District Patricia Huberty Comer Elementary School Andrew Isaacs University of Chicago Andrew Izsak University of Georgia Henry Kepner University of Wisconsin Catherine Lewis Mills College William Lewis University of Nebraska James Madden Louisiana State University William McCallum University of Arizona Raven Mccrory Michigan State University Aki Murata Stanford University Anderson Norton Virginia Polytechnic Institute and State University Randolph Philipp San Diego State University Marc Roth San Francisco Unified School District Susan Jo Russell TERC Deborah Schifter Education Development Center Sharon Senk Michigan State University Katherine Socha Math for America Denise Spangler University of Georgia Maria Tatto Michigan State University Andy Tyminski Clemson University Kristin Umland University of New Mexico Zalman Usiskin University of Chicago W Stephen Wilson Johns Hopkins University Officially Registered Participants First Name Last Name Current Institution Sarah Alford UC Berkeley Emina Alibegovic University of Utah David Auckly Mathematical Sciences Research Institute Elizabeth Baker Mills College, School of Education Sybilla Beckmann University of Georgia Lisa Berger SUNY Mariah Birgen Wartburg University Richard Bisk Worcester State University Diane Briars National Council of Supervisors of Mathematics Stacy Brown Pitzer College Heidi Burgiel Bridgewater State University Heather Calahan University of California, Los Angeles Jamye Carter Alabama State University Jamylle Carter San Francisco State University David Chosa Sonoma County Office of Education Thomas Clark University of Nebraska Herbert Clemens Ohio State University Amy Cohen Rutgers University Jung Colen Indiana University of Pennsylvania Yong Colen Indiana University of Pennsylvania Jane Decker-Baldwin Petaluma High School Josh Deis Sonoma State University Lew Douglas University of California, Berkeley Jerry Dwyer Texas Tech University Joan Easterday Sonoma County Office of Education Joan Ferrini-Mundy National Science Foundation Ben Ford Sonoma State University Astrid Fossum Milwaukee Public Schools David Foster Silicon Valley Mathematics Initiative Shelley Friedkin Mills College Suzanne George Tomlin Middle School Sandra Gilliam Colorado College E. Paul Goldenberg Center for Mathematics Education Concha gomez Los Medanos College Emiliano Gomez University of California, Berkeley Melissa Hedges Mequon-Thiensville School District First Name Last Name Current Institution Ola Helenius University of Göteborg Aloysius Helminck North Carolina State University jennifer hogan Skyline High School Lisa Holmes Richmond High School Patricia Huberty Comer Elementary School Cathy Humphreys Stanford University Jacqueline Hurd Addison School Andrew Isaacs University of Chicago Andrew Izsak University of Georgia Anette Jahnke Goteborg University Melissa Jay Adobe Systems Incorporated Gail Johnston Iowa State University Thomas Judson Stephen F. Austin State University Melissa Kemmerle Stanford University Henry Kepner University of Wisconsin Cathy Kessel Association for Women in Mathematics Kurt Kreith University of California, Davis Brigitte Lahme Sonoma State University Kathlan Latimer California Mathematics Council Catherine Lewis Mills College William Lewis University of Nebraska Joanne Lieberman California State University Monterey Bay Mark Lobaco Kennedy High School James Madden Louisiana State University William McCallum University of Arizona raven mccrory Michigan State University Julie McNamara Math Solutions Robert Megginson University of Michigan Richard Millman Georgia Institute of Technology Erik Moll California State University Ann (Sage) Moore Skyline High School Kathy Morris Sonoma State University Katie Morrison University of Nebraska Gretchen Muller California Mathematics Council Aki Murata Stanford University Anderson Norton Virginia Polytechnic Institute and State University Rodrigues NSUKA Unniversity of Kinshasa First Name Last Name Current Institution Rebeccai Perry Mills College Stan Pesick Oakland Unified School District Randolph Philipp San Diego State University Kathleen Pitvorec University of Illinois Bindu Pothen Stanford University Tom Roby University of Connecticut Marc Roth San Francisco Unified School District Susan Jo Russell TERC Deborah Schifter Education Development Center Daniel Schultz-Ela Mesa St College Leslie Sena Cookman College Sharon Senk Michigan State University Meghan Shaughnessy University of Michigan Helen Smiler Project SEED Marianne Smith Marianne Smith, Consultant Katherine Socha Math for America Tracy Sola Ralston Intermediate Denise Spangler University of Georgia Dick Stanley University of California Maria Tatto Michigan State University Andy Tyminski Clemson University Zalman Usiskin University of Chicago Diana White University of Colorado, Denver Gregory White Notre Dame de Namur University Ellen Whitesides Harvard University Brandy Wiegers Mathematical Sciences Research Institute marlene wilson hillcrest school, Oakland, CA W Stephen Wilson Johns Hopkins University Risa Wolfson Lawrence Hall of Science Justine Wong Redwood High David Wright Brigham Young University

Critical Issues in Mathematics Education Series The Mathematical Education of Teachers May 11 - 13, 2011

Schedule

Wednesday, May 11, 2011 4:00 – 4:30PM Simons Auditorium Introduction and Overview

4:30 – 5:00PM Simons Auditorium William McCallum The Impact of the Common Core State Standards on the Education and Professional Development of Teachers 5:00 – 6:30PM Atrium Reception and Light Buffet Dinner 6:30 – 7:00PM Simons Auditorium Denise Spangler Why Content Knowledge Matters in Teaching and the Implications for Teacher Education 7:00 – 7:30PM Simons Auditorium Diane Briars

7:30 – 7:45PM Atrium Break

7:45 – 8:15PM Simons Auditorium Deborah Ball Learning to Teach Something in Particular: How the Common Core Can Leverage Radical Improvement in Teacher Training

Thursday, May 12, 2011 8:00 – 8:30AM Atrium Coffee and Tea

8:30 – 10:00AM Simons Auditorium Sybilla Beckmann How Can the Community of All Mathematics Catherine Lewis Teachers Work Together and Learn From Each Other to Improve Mathematics Teaching? 10:00 – 10:30AM Atrium Break 10:30 – 12:00PM Simons Auditorium Zalman Usiskin Panel on Curriculum and Teacher Education in Paul Goldenberg Light of Common Core – Comments From Andy Isaacs Curriculum Developers 12:00 – 1:30PM Atrium Lunch

1:30 – 3:00PM Simons Auditorium Susan Jo Russell Early Algebra and the Common Core: What Do Deborah Schifter Teachers Need to Know? 3:00 – 4:00PM Atrium Coffee and Tea

4:00 – 5:30PM Simons Auditorium Raven McCrory Research Findings About Teacher Education Sharon Senk Maria Teresa Tatto

Friday, May 13, 2011 8:00 – 8:30AM Atrium Coffee and Tea 8:30 – 9:00AM Simons Auditorium Joan Ferrini-Mundy Common Core Implementation and the Mathematical Education of Teachers: Policy Perspectives and Support 9:00-10:00AM Simons Auditorium Aki Murata Panel on Curricula and Teacher Learning W. Stephen Wilson 10:00 – 10:30AM Atrium Break 10:30 – 12:00PM Breakout Sessions Simons Auditorium Lesson Study Models: What Models of Mathematics Lesson Study Have Emerged in the U.S. and What Can They Each Contribute? Library Jim Lewis Interactive Session: Improving Teacher Education Kristin Umland Baker Board Room Herbert Clemens Teacher Education and Professional Development James Madden Atrium Anderson Norton Findings from Mathematics Education Research Andrew Izsak 12:00 – 1:30PM Atrium Lunch 1:30 – 3:00PM Breakout Sessions Simons Auditorium Lesson Study: Advice from K-12 and University-Based Lesson Study Practitioners Commons Randolf Philipp How A Focus on Children’s Mathematical Thinking Supports the Professional Development of Elementary School Teachers Baker Board Room Richard Bisk Teacher Education and Professional Development Katherine Socha Library Paul Goldenberg Interpreting the Mathematical Practices of the Common Core State Standards for the Elementary and Middle Grades Atrium Zalman Usiskin Recruiting More Students into Mathematics Teaching 3:00 – 3:30PM Atrium Coffee and Tea 3:30 – 4:15PM Breakout Session Library Robert Farinelli The Role of Two-Year Colleges in Teacher Preparation Commons Henry Kepner Teachers Reflect on the Mathematics They Need to Melissa Hedges Teach Their Students Astrid G. Fossum Atrium Marc Roth A Teacher’s Perspective: The Help That I Have Received and Not Received from the Mathematical Community Video Room Patti Huberty A Teacher’s Perspective on Daily Professional Development: How do We Utilize Our Classroom Experiences to Gain Mathematical Understanding and Enhance Future Instruction? IT Conference Jerry Dwyer The Perspective of an Outreach Mathematician: Bridging the Gap Simons Auditorium Andrew Tyminski Developing Pre-Service Elementary Mathematics Teacher’s Knowledge Bases Through Standards-Based Curriculum Materials Baker Board Room David Foster Inside Mathematics Dot Com 4:15 – 4:30PM Atrium Break 4:30 – 5:15PM Simons Auditorium Jim Lewis Follow-Up Efforts to the Common Core State Standards William McCallum 5:15 – 5:45PM Simons Auditorium Herbert Clemens Closing Remarks: Common Core Mathematics Standards and Teacher Professional Development 5:45 – 7:00pm Atrium Reception

Officially Registered Participant Information Participants 105

Gender 105 Male 39.05% 41 Female 60.95% 64 Declined to state 0.00% 0

Ethnicity* 105 White 79.05% 83 Asian 4.76% 5 Hispanic 6.67% 7 Pacific Islander 0.00% 0 Black 3.81% 4 Native American 1.90% 2 Declined to state 3.81% 4 * ethnicity specifications are not exclusive

Probability Workshop: 2010 PIMS Summer School in Probability June 21, 2010 to July 10, 2010 University of Washington and Microsoft Research, Seattle, WA, USA

Organizers: Krzysztof Burdzy (University of Washington) Zhenqing Chen (University of Washington) Christopher Hoffman (University of Washington) Soumik Pal (University of Washington) Yuval Peres ( University of California, Berkeley)

Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Final report MSRI Graduate Summer Workshop combined with 2010 Paciﬁc Institute for the Mathematical Sciences Summer School in Probability June 21 – July 10, 2010

Organizers: K. Burdzy, Z.-Q. Chen, C. Hoﬀman, S. Pal (University of Washington), Y. Peres (Microsoft Research)

The 2010 Pacific Institute for the Mathematical Sciences (PIMS) Summer School in Probability was held at the University of Washington and Microsoft Research from June 21 to July 10, 2010. The school was devoted to training of doctoral students in the area of probability. Participants included graduate students, advanced undergraduate students, recent Ph.D.’s, and also regular faculty. The 2010 School was the fifth event in a series of PIMS Summer Schools in Probability. The first four were held in Vancouver at the University of British Columbia. There were about 150 participants, of which about 100 received financial support for lodging and (some) meals from the following sources: Mathematical Sciences Research Institute, Microsoft Research, Milliman Fund at the Mathematics Department, Univer- sity of Washington, National Science Foundation, National Security Agency, Pacific In- stitute for Mathematical Sciences and Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) grant at the Mathematics Department, University of Washington. Some of them, mostly supported by MSRI, also received travel support. About 20 participants were based at the University of Washington and Microsoft Research (both located in Seattle, WA), and about 130 participants came from other cities in the US and abroad. The program consisted of two main courses, 15 lecture long each, and three short courses, 5 lecture long each. In addition, every course was accompanied by tutorial sessions. Each lecture was 50 minutes long. Participants (students) had a chance to present the results of their own research by giving 25-minute contributed talks. There were about 30 contributed talks. The main courses and their contents were the following. 1. Exchangeable Coalescents by Jean Bertoin In a celebrated work Kingman constructed a remarkable coalescent process which is related to the genealogy of certain large population models. Möhle,Pitman, Sagitov and

Page 2 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Schweinsberg introduced a natural extension of Kingman’s coalescent, called exchangeable coalescents. Roughly speaking, an exchangeable coalescent describes the evolution of a particle system in which particles coagulate as time passes. The coagulations can be both multiple (i.e. involve more than two particles) and simultaneous (i.e. several clumps of particles can merge at the same time), and enjoy an important property of exchangeability. The purpose of this mini-course is to introduce the main aspects of this theory as well as some recent developments. It is largely based on chapters 2 and 4 of Bertoin’s monograph and a series of joint works of Bertoin with Jean-Francois Le Gall in which the connection between exchangeable coalescents and certain stochastic flows of bridges is developed. The theory leads to several interesting applications, for instance to the asymptotic behavior of these coalescents, and to an interpretation of a version of Smoluchowski’s coagulation equation with multiple coagulations. 2. Random surfaces and quantum gravity by Scott Sheffield What is the most natural notion of a “random” two dimensional manifold? This question is inspired by modern physics, where many problems involve “integrating” over a space of two dimensional Riemannian manifolds. The physics literature has explored various answers to this question, including non-rigorous derivations via conformal field theory. This course gave an overview of recent mathematical work in the area. It discussed both discretized random surfaces (based on so-called random planar maps) and continuum random surfaces (the so-called Liouville quantum gravity), as well as the connection between the two. Topics included tree bijections (the Schaeffer correspondence and the Bernardi correspondence), the Brownian map, the Gaussian free field, the KPZ formula, the Schramm-Löwnerevolution, and conformal welding. The short courses and their contents were the following. 1. Dirichlet Form Theory and Invariance Principle by Zhenqing Chen The theory of Dirichlet forms provides a powerful connection between probabilistic and analytic potential theory. It is also an effective machinery for studying various stochastic models, especially those with non-smooth data, on fractal-like spaces or spaces of infinite dimensions. In this mini course, Chen gave a quick introduction to the basic theory of Dirichlet forms, and illustrated it with the recently developed applications of the theory to various invariance principles for stochastic processes.

Page 3 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

2. Scaling Limits and SLE by Gregory Lawler This was an introduction to lattice models in statistical physics and their scaling limits in two-dimensions (Schramm-Loewner evolution and loop measures). This course was coordinated with Scott Sheffield’s course — the intent was for this course to be more introductory and Sheffield’s course to be more advanced and specialized. 3. Mixing Times of Markov Chains by Eyal Lubetzky, Yuval Peres and David Wilson Markov Chains are one of the most important objects in probability theory. They are used in theoretical mathematics as well as many branch of applied mathematics, including statistical physics, mathematical biology, statistics, economics and other fields. A Markov chain is a stochastic process with the property that conditioned on the present state of the process that the future states are independent of the past states of the process. Under mild regularity conditions, a Markov chain with a finite state space converges to a unique stationary distribution. For a Markov chain the mixing time tells steps needed to get the distribution rea- sonably close to its limit. In 1986 Aldous and Diaconis presented the concept of mixing times to a wider audience, using card shuffling as a central example. Since then, both the field and its interactions with computer science and statistical physics have grown tremen- dously. There are now many methods for determining the mixing time of a Markov chain as a function of the geometry and size of the state space. This short course surveyed these methods and highlighted their applications.

Lawler’s lectures played a double role of a stand-alone short course on SLE and an extra tutoring for students taking Sheffield’s advanced course. Since the Workshop attracted a very large audience (about 150 participants), there were naturally groups interested to greater degree in one of the main courses. A number of participants took very active attitude towards the school, for example, by solving homework problems posted by Sheffield and by meeting informally after hours. The Summer School Web site (http://pims2010.web.officelive.com/) proved to be the hub of various activities. New material was posted daily, from lecture notes prepared by the instructors, homework problems and their solutions and schedule of scientific activities, to practical information and recreation. The results of a confidential online survey conducted by PIMS are enclosed as a separate document. They confirm the anecdotal evidence of very high satisfaction with the contents of the courses and effectiveness of the school.

Page 4 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Additional information (a) List of attendants to the workshop – see the attached Excel ﬁle (pdf version is also enclosed)

(b) List of lecturers, organizers, and tutors Main courses instructors * Jean Bertoin (Universit´ePierre et Marie Curie) * Scott Sheﬃeld (MIT) Short courses instructors * Zhenqing Chen (University of Washington) * Greg Lawler (University of Chicago) * Eyal Lubetzky, Yuval Peres, David Wilson (Microsoft Research) Tutors * Tom Alberts (University of Toronto) * Mauricio Duarte (University of Washington) * Shuwen Lou (University of Washington) * Asaf Nachmias (MIT) * Douglas Rizzolo (University of California, Berkeley) * Brent Werness (University of Chicago)

(c) The titles, instructors and course content are listed above. The daily schedule was: 9:00-9:50 Main course I 10:00-10:30 Coﬀee break 10:30-11:20 Main course II 11:30-12:20 Short course on the middle day of the week; Tutorial on other days 12:30-2:00 Lunch break 2:00-2:50 Short course 2:50-3:20 Coﬀee break 3:20-4:10 Tutorial for short course alternated with a participant talk 4:10-5:00 Participant talks

Page 5 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Invited Participants

firstname lastname institutionname Prakas Balachandran Duke University Nishant Chandgotia University of British Columbia Ajay Chandra University of Virginia Sha Chang California Institute of Technology Shawn Drenning University of Chicago Aaron Dutle University of South Carolina Sukhada Fadnavis Stanford University Jon Fickenscher Rice University Fang Gu University of Toronto Xiaoqin Guo University of Minnesota Twin Cities Boris Hanin Northwestern University Benjamin Katz-Moses University of Colorado Elisabeth Kemajou Southern Illinois University Eun Kim University of Colorado Jung Eun Kim The Ohio State University Timur Kupaev University of Notre Dame Zhongyang Li Brown University Hao Lin University of Wisconsin Weihua Lin University of Oklahoma Shitao Liu University of Virginia Zhi Liu Hong Kong University of Science and Technology Shishi Luo Duke University Nicole Meyer Tulane University Hyungju Park University of Illinois at Urbana-Champaign Bernardo Reis Carneiro da Costa Lima McMaster University Douglas Rizzolo University of California, Berkeley Brian Simanek California Institute of Technology Erin Solfiell North Carolina State University Russ Thompson Cornell University Alexander Vandenberg-Rodes University of California, Berkeley Jeremy Voltz University of Toronto Zhihui Xie Dept. of Math, The Univ. of Texas at Austin Linwei Xin Georgia Institute of Technology Fang Xu McMaster University Zhe Xu University of California, Berkeley Gokhan Yildirim University of Southern California

Page 8 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Invited Participants

firstname lastname institutionname Jun Zhang Arizona State University Xiaojing Zhang Kansas State University Tianyi Zheng Cornell University

Page 9 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Officially Registered Participant Information Participants 39

Gender 39 Male 64.10% 25 Female 33.33% 13 Declined to state 2.56% 1

Ethnicity* 39 White 33.33% 13 Asian 61.54% 24 Hispanic 0.00% 0 Pacific Islander 0.00% 0 Black 2.56% 1 Native American 0.00% 0 Declined to state 2.56% 1 * ethnicity specifications are not exclusive

Page 10 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

99 responses

Summary See complete responses

How did you hear about his event? Colleague 28 28% Advisor 51 52% Professional publication 4 4% Internet 20 20% PIMS publication 1 1% PIMS website 10 10% Poster 4 4% Other 9 9%

People may select more than one checkbox, so percentages may add up to more than 100%.

Organization

Please rate each of the following aspects of the event you attended. [If an item does not apply to your event, just leave it blank.]

Pre-event communication and support 1 - Very dissatisfied 0 0% 2 1 1% 3 7 7% 4 37 39% 5 - Very satisfied 49 52%

Very dissatisfied Very satisfied

Page 12 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

PIMS website usefulness 1 - Very dissatisfied 0 0% 2 1 1% 3 7 7% 4 20 21% 5 - Very satisfied 69 71%

Very dissatisfied Very satisfied

Registration/reception organization 1 - Very dissatisfied 0 0% 2 2 2% 3 12 13% 4 32 34% 5 - Very satisfied 48 51%

Very dissatisfied Very satisfied

Event venue 1 - Very dissatisfied 0 0% 2 2 2% 3 5 5% 4 37 40% 5 - Very satisfied 48 52%

Very dissatisfied Very satisfied

Food/catering

Page 13 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

1 - Very dissatified 3 3% 2 14 15% 3 29 31% 4 30 32% 5 - Very satisfied 19 20%

Very dissatified Very satisfied

Accommodation 1 - Very dissatisfied 2 2% 2 14 16% 3 34 38% 4 25 28% 5 - Very satisfied 15 17%

Very dissatisfied Very satisfied

Social functions 1 - Very dissatisfied 2 2% 2 7 8% 3 22 24% 4 34 37% 5 - Very satisfied 28 30%

Very dissatisfied Very satisfied

Audio/Visual capabilities and support

Page 14 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

1 - Very dissatisfied 0 0% 2 4 4% 3 9 10% 4 30 32% 5 - Very satisfied 51 54%

Very dissatisfied Very satisfied

Scheduling 1 - Very dissatisfied 0 0% 2 5 5% 3 11 12% 4 29 31% 5 - Very satisfied 50 53%

Very dissatisfied Very satisfied

Reasonableness of financial support (if any) 1 - Very dissatisfied 1 1% 2 4 5% 3 5 6% 4 16 20% 5 - Very satisfied 55 68%

Very dissatisfied Very satisfied

Post-event support

Page 15 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

1 - Very dissatisfied 0 0% 2 1 1% 3 17 25% 4 23 34% 5 - Very satisfied 26 39%

Very dissatisfied Very satisfied

Event Content

Please rate the quality or potential value of each of these aspects of the event you attended. [If an item does not apply to your event, just leave it blank.]

Timeliness and importance of the program topic 1 - Low 0 0% 2 1 1% 3 7 7% 4 43 45% 5 - High 45 47%

Low High

Novelty of program topic 1 - Low 0 0% 2 0 0% 3 8 8% 4 37 38% 5 - High 52 54%

Low High

Page 16 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Quality of presenters/presentations 1 - Low 0 0% 2 1 1% 3 7 7% 4 45 46% 5 - High 44 45%

Low High

Potential to enhance your work/research/education 1 - Low 1 1% 2 2 2% 3 11 11% 4 49 51% 5 - High 34 35%

Low High

Potential for future collaborative interactions 1 - Low 1 1% 2 5 5% 3 25 26% 4 40 41% 5 - High 26 27%

Low High

Potential for inter-disciplinary applications

Page 17 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

1 - Low 3 3% 2 13 14% 3 27 28% 4 29 30% 5 - High 24 25%

Low High

Potential for advancing the field 1 - Low 1 1% 2 2 2% 3 19 20% 4 35 37% 5 - High 38 40%

Low High

Overall Evaluation

Please rate your overall level of satisfaction with each of the following aspects of the event you attended.

Event Organization 1 - Poor 0 0% 2 0 0% 3 4 4% 4 49 50% 5 - Excellent 45 46%

Poor Excellent

Page 18 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Event Content 1 - Poor 0 0% 2 1 1% 3 8 8% 4 42 43% 5 - Excellent 47 48%

Poor Excellent

Overall satisfaction with the event 1 - Very dissatisfied 0 0% 2 1 1% 3 3 3% 4 46 47% 5 - Very satisfied 47 48%

Very dissatisfied Very satisfied

General comments, observations and suggestions for improvements: It would be nice if the instructors spent more time motivating the subject and reminding students of the original reason for studying the field and how everything connects back. Also, a short tutorial in stochastic calculus for students without that background would have been useful. Professor Jean Bertoin is an excellent teacher. I very much enjoyed attending his lectures. Other conferences/summer schools I've been to have given out a list of participants along with their institutions and/or email address which is often helpful in getting to know people at the beginning of the school ...

What would you say was the scientific highlight of the event? I enjoyed Scott Sheffield's course. The notes and reading materials provided for each of the courses were of a very high quality and will be useful in exploring each of the topics in more detail after I return to my home institution. Prof. Bertoin's lectures were excellent. He explained the difficult concepts very well and introduced the theory from the beginning and developed gradually very well. I think he is definitely the best lecturer of the summer school. His TA was also very good. Prof. Lawler's lectures are very good too. I think we needed more time for that course.His TA was also ...

What topics would you like to see covered in future PIMS events?

Page 19 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

topic at interface among statistical physics, probability and computer science More mixing times, statistical physics methods in probability, more connections with combinatorics. More on conformally invariant processes. stochastic partial differential equations (perhaps as possible speakers: Krylov, Gyöngy, Röckner) I would like to see a three weeks course on SLE by Lawler assisted with a TA. Since SLE is an active current research area, starting from the elementary concepts of the field and gradually developing the theory in a three week period would be great. Every day one lecture delivere ...

Number of daily responses

Page 20 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 11 65% partially 6 35% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? above satisfactory 7 41% satisfactory 10 59% not satisfactory 0 0% no opinion 0 0%

Was there too much material presented; was the workshop too ambitious?

Page 21 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research too much 5 29% just right 12 71% not enough 0 0% no opinion 0 0%

Was the problem session helpful? yes 8 47% partially 6 35% no 1 6% no opinion 2 12%

Additional comments on the topic presentation and organization i think there should be less topics but more focused and detailed Problem Sets were super helpful. Not all of the problem session leaders were prepared

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 12 71% partially 4 24% no 1 6%

Page 22 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research Did the workshop increase your interest in the subject? yes 14 82% partially 3 18% no 0 0%

Was the workshop worth your time and effort? yes 14 82% partially 3 18% no 0 0%

Is it likely that you will work in the area of the workshop subject in the future? yes 9 53% partially 7 41% no 1 6%

How would you evaluate your interaction with other participants?

Page 23 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research 1 - above satisfactory 4 24% 2 7 41% 3 6 35% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Page 24 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research

Additional comments on your personal assessment The general strength of students was quite low.

Venue

Please rate the different categories

Your overall experience 1 - above satisfactory 6 35% 2 8 47% 3 1 6% 4 2 12% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The assistance provided by staff 1 - above satisfactory 10 59% 2 4 24% 3 1 6% 4 2 12% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The physical surroundings

Page 25 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research 1 - above satisfactory 7 41% 2 5 29% 3 2 12% 4 3 18% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on the venue thanks. everything was great It would have been very nice to have the program arrange access to the gym for the summer. I wish there were an easier way to print

Accommodation and Food

Please rate the different categories

The summer school accommodation 1 - above satisfactory 3 18% 2 4 24% 3 6 35% 4 3 18% 5 - not satisfactory 1 6%

above satisfactorynot satisfactory

The food provided

Page 26 of 27 Probability workshop: 2010 PIMS Summer School in Probability, June 21, 2010 to July 10, 2010 at the University of Washington and Microsoft Research 1 - above satisfactory 3 18% 2 5 29% 3 5 29% 4 4 24% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on accommodation and food Cafeteria food: at least there's always a healthy salad option. I wish not everything were fried.

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. this is very good summer school

Number of daily responses

Page 27 of 27

Mathematics of Climate Change July 12, 2010 to July 23, 2010 National Center for Atmospheric Research Boulder, Colorado, USA

Organizers: Chris Jones (University of North Carolina and University of Warwick) Doug Nychka (National Center for Atmospheric Research) Mary Lou Zeeman (Bowdoin College)

Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

Final Report: Summer School on Mathematics and Climate Change 2010

Organizers

Mary-Lou Zeeman (Bowdoin College and Cornell University), Chris Jones (UNC-CH and University of Warwick), and Douglas Nychka (National Center for Atmospheric Research)

Background:

It is generally accepted in the scientific community that the world is undergoing a significant change in its climate. Mathematical models play a central role in climate change research. The goal of this summer graduate workshop is to introduce students to some of the central ideas and techniques of mathematical climate science and engage them in the process of uncovering the key mathematical problems of the area. It is also an opportunity for students to meet peers from diverse backgrounds in the mathematical sciences and gain experience working as a team on projects

A two week summer school was held at the National Center for Atmospheric Research (NCAR) Boulder, CO, from July 12 to 23, 2008. This activity was a partnership between MSRI, the mathematics and climate research network (MCRN), and the Institute for Mathematics Applied to Geoscinces (IMAGe) and capped the Theme-of-the-Year Program on Mathematicians and Climate at NCAR.

The summer school was a highly successful event energizing a new generation of mathematical scientists to contribute to climate mathematics.

Objectives of Summer School:

We had two main objectives in running this summer school:

• To define specific problems that are both amenable to mathematical investigation and of great relevance to the pressing issues of climate change, and

• To excite the students attending the summer school about these problems, give them the basic tools and understanding to both contribute themselves to this area and to go back to their home institutions and share this knowledge.

Structure of Summer School:

The first week of the workshop was an organized program of lectures, attendant discussions and computer labs. Saturday after the first week included a field trip to the Colorado Alpine Research Station for the students to see first hand how long term climate measurements are made and to appreciate the difficulties of taking observations. The first week schedule is listed below to give an impression of the broad scope of the school and the diversity of lecturers. During the second week, the school switched to independent student research projects. Also interspersed in this time were some lectures by prominent researchers (Eli Tziperman ,Harvard and Ken Golden, Univ. Utah ) to showcase the interplay between mathematical modeling and understanding particular geophysical processes. The projects were

Page 3 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

computationally based, with the school providing individual student MATLAB licenses when needed. The students collaborated in teams and were guided by both early career and senior researchers.

Student projects ranged from exploring concepts of uncertainty through a stochastic Lorenz system to

modeling the feedback loop between global average temperature and atmospheric CO2; time series analysis of the ice core data; and data assimilation for climate systems. The enthusiasm and energy level was easy to discern over the course of the two weeks, and it was clear Climate Mathematics can indeed provide a focus for graduate mathematical research. Several of the projects have formed the basis for ongoing working groups, conducted over the internet.

Schedule Week 1.

Monday July 12. Introduction to Climate • A: Dynamics the Earth's climate system, Doug Nychka • B: Present and past Climate, Pam Martin • C: Structure and chemistry of the atmosphere, Laura Voss • Lab: Matlab Intro/Review Maartin Arnst

Tuesday July 13. Simple models for climate dynamics and equilibria • A: Energy balance models, Richard McGehee • B: A Jormungand solution to the snowball paradox? Dorian Abbott • C: Tipping points in a simple model of Arctic sea ice, Mary Silber • Lab: Simple models Esther Widiasih

Wednesday July 14. Looking at climate data • A: EOFs and spatial data, Doug Nychka • B: Decompositions of fields, David Camp • C: Combining data and models, Chris Danforth • Lab: Interpreting spatial data and time series, King-Fai Li

Thursday July 15. Intermediate climate models. • A: Geophysical fluid dynamics, Chris Jones • B-C: MIT GCM, Chris Forest • Lab: Adrean Webb

Friday July 16. Choosing projects • A: Topics using models • B: Topics using data • C: Project discussion • Lab: Small group meetings

Page 4 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

Description of Student Research Projects

Models and Data Analysis

MIT IGSM “Mod Squad” (David, Alyssa, Kevin) This group experimented with the MIT Integrated Global System Model to see whether a Jormungand state arises under appropriate climate conditions (varying CO2 and faint young sun). Note: the Jormangund state, coined by Dorian Abbot, refers to a partially Snowball earth with a ribbon of “slush” rather than ice at the equator. An ice line at 45 degrees was observed, but the experiment was not run for long enough foe the ocean to equilibrate.

EMD “Hot Earth” (Agnes, Jason) This group condicted a time series analysis, using empirical mode decomposition (EMD), of O18 data from last 60 million years. From 0 to 38 million years ago there was ice. Before that there was no ice. For each mode extracted by EMD, an FFT was run. Using the full data set, 41Ky (obliquity), 100Ky (eccentricity) and 400Ky (eccentricity) cycles are visible. Using early data (no ice), 400Ky cycles dominate. Using recent data (ice) 41Ky cyckes dominate. Using very recent data (500Ky) 100Ky cycles dominate. These preliminary results are so interesting that an MCRN working group has grown out of the project.

“Newby” (Chong, Yang) This group experimented with temporal empirical orthogonal function (EOF) methods applied to 2001- 2005 vegetation index data from the Harvard Forest.

“Red Noise” (Matt, Manuel) This group experimented with EMD and EOF methods to extract modes from spatio-temporal precipitation and aerosol data.

Data Assimilation and Prediction

“Twin” Extended Kalman Filter (Darin, Tom) This group compared Kalman filter, ensemble Kalman Filter, and extended Kalman Filter techniques for data assimilation. The methods were applied to the Lorentz 63 model of chaotic weather, and to the

Hogg 2007 model of temp and CO2 feedback under driving by Milankovitch cycles.

“RAD” (Rachel, Daniel) This group experimented with particle filters for data assimilation. The approach relaxes the linear and Gaussian assumptions of the Kalman filter, but is computationally costly in high dimensions.

“MCMC” (Sebastian, Adam, James) This group experimented with filtering and data assimilation methods for inverse problems in stochastic ODEs. The goal is to deduce distributions for model parameter values from the observations.

“BIG” (Bin, Zhao, Nan) This group applied data assimilation methods to inverse problems (as in MCMC group). The methods were tested on a simplified carbon dynamic model of Raupach 2007.

Dynamics of Climate

Page 5 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

“Solo” (Kasia) Kasia investigated the invariant Sinai-Ruelle-Bowen measure and ergodic theory for the Lorenz system, and worked towards a computational approach for estimating the measure.

“Thor” (Tim, Andrew, Philip, Francesco) This group used the one-dimensional, radially symmetric, Budyko energy-balance model to investigate the Jormungand state proposed by Dorian Abbot. The model is generalized to include three surface coverings for the earth (ice, snow and water). The albedo discontinuity in Abbot’s model was resolved in a variety of ways to explore conditions under which the Jormungand state arises.

“Delicious” (Colleen, Julia, Alena) This group modeled the interaction between agricultural emissions from food production, temperature and arable land-use projections, UN population projections, and dietary composition.

“Spicy” (Lei, Yu-Min, Le) This group used the Budyko model to explore the effect of varying atmospheric CO2 and possible water vapor feedback on ice line and global temperature.

“Passport” (Pietro, Raj, Anastasia) This group modeled the effect of the antarctic circumpolar current (ACC) on the meridional overturning circulation (MOC) using a box ocean model of the north atlantic. They explored the effect of wind driven forcing of the ACC on the MOD, to investigate sea ice feedback in glacial vs. interglacial periods. Interesting transitions were observed between stability and relaxation oscillations as forcing varies. Raj has further developed many of these ideas in his PhD thesis (2011). He will be an Ed Lorenz postdoc with MCRN from Fall 2011, and will establish an MCRN working group to continue related projects.

“ANTCM” (Andrew, Felicia) This group explored zero-dimensional energy balance models analytically. The models were forced with sinusoidal fittings of paleoclimate solar data, and with linear fitting of radiative forcing over the last half century.

“Awesome” (Genna, Anna, Samantha, Genevieve, Jessica, Esther, Talea) This group started from work of Esther Widiasih that extends Budyko’s one-dimensional energy balance

model to include a dynamic ice line. The group added an equation for CO2 (inspired in part by a 2007 paper by Hogg), and feedback between CO2 and temperature. They found intrinsic oscillations with period approx. 100Kyr, without any Milankovitch cycle forcing. These preliminary results are so interesting that an MCRN working group has grown out of the project.

“Mini-Awesome” (Diego, Sarah) This group expanded the one-dimensional Budyko model to include short term carbon cycling, and to explore a diffusive transport term in place of the relaxation term.

“Intergroup” (Sarah, Diarmuid) This group developed Matlab and Mathematica structures to encompass many variations on the one- dimensional (radially symmetric) Budyko theme. A Budyko “master function” was written, and the structure developed so that models for the albedo, carbon evolution, ice line motion, temperature transport, incoming and outgoing radiation and greenhouse gas effects can be individually developed

Page 6 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

and inserted in the master function. The code will be documented and posted for public use.

Web-site and internet support

Throughout the summer school, an extremely useful dynamic website and wiki was maintained by the Teaching Assistants. Lecture notes and matlab files were posted daily, together with useful literature, links, and working notes of the groups.

Page 7 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

Invited Participants

firstname lastname institutionname Jason Atnip Baylor University Diego Ayala McMaster University Anna Barry Boston University Agnes Beaudry Northwestern University Thomas Bellsky Michigan State University Francesco Bonghi Università di Roma ``La Sapienza'' Yu-Min Chung Indiana University David Collins University of Southern California Darin Comeau University of Arizona Rachel Danson California State University Bin Deng Indiana University Timothy Dorn University of Kansas Daniel Jordon Drexel University Chong Liu Boston University Adam Mallen Marquette University Alena Maze Georgetown University Colleen McCarthy North Carolina State University James Melbourne University of Minnesota Twin Cities Matthew Norman North Carolina State University Samantha Oestreicher University of Minnesota Twin Cities Alyssa Pampell Southern Methodist University Pietro Peterlongo École Normale Supérieure Andrew Roberts University of North Carolina Raj Saha University of North Carolina Felicia Tabing University of California, Berkeley Lei Wang University of Michigan Katarzyna Wasilewska University of Southern California Anastasia Yanchilina Creighton University Zhao Yang Baylor University Yang Zou University of Regina

Page 8 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

Invited Participants Participants 30

Gender 30 Male 60.00% 18 Female 40.00% 12 Declined to state 0.00% 0

Ethnicity* 30 White 63.33% 19 Asian 23.33% 7 Hispanic 3.33% 1 Pacific Islander 0.00% 0 Black 6.67% 2 Native American 0.00% 0 Declined to state 3.33% 1 * ethnicity specifications are not exclusive

Page 89 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 13 87% partially 2 13% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? above satisfactory 10 67% satisfactory 5 33% not satisfactory 0 0% no opinion 0 0%

Was there too much material presented; was the workshop too ambitious?

Page 11 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado too much 2 13% just right 13 87% not enough 0 0% no opinion 0 0%

Was the problem session helpful? yes 11 73% partially 2 13% no 1 7% no opinion 1 7%

Additional comments on the topic presentation and organization derivation of fluid mechanics equations was fantastic! I found the question and answer sessions particularly helpful, because they gave us a chance to clear up some fundamental questions that were so ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 11 73% partially 3 20% no 1 7%

Page 12 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado Did the workshop increase your interest in the subject? yes 13 87% partially 2 13% no 0 0%

Was the workshop worth your time and effort? yes 15 100% partially 0 0% no 0 0%

Is it likely that you will work in the area of the workshop subject in the future? yes 6 40% partially 9 60% no 0 0%

How would you evaluate your interaction with other participants?

Page 13 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado 1 - above satisfactory 5 33% 2 8 53% 3 0 0% 4 2 13% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Page 14 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado

Additional comments on your personal assessment I had less experience than I thought I had so I had trouble grasping the first few lectures since they dove right into the lectures using words and phrases that I did not understand as a pure math s ...

Venue

Please rate the different categories

Your overall experience 1 - above satisfactory 12 80% 2 1 7% 3 0 0% 4 2 13% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The assistance provided by staff 1 - above satisfactory 9 60% 2 4 27% 3 0 0% 4 1 7% 5 - not satisfactory 1 7%

above satisfactorynot satisfactory

The physical surroundings

Page 15 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado 1 - above satisfactory 12 80% 2 1 7% 3 0 0% 4 1 7% 5 - not satisfactory 1 7%

above satisfactorynot satisfactory

Additional comments on the venue holding the workshop at the NCAR Mesa Lab instead would be great! Staff was extremely helpful in helping me to bookkeeping that I needed to do! Boulder is gorgeous. And the foothills lab provided a re ...

Accommodation and Food

Please rate the different categories

The summer school accommodation 1 - above satisfactory 4 27% 2 8 53% 3 0 0% 4 3 20% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The food provided

Page 16 of 16 Mathematics of Climate Change, July 12, 2010 to July 23, 2010 at National Center for Atmospheric Research (NCAR) in Boulder, Colorado 1 - above satisfactory 3 20% 2 8 53% 3 2 13% 4 2 13% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on accommodation and food stipend was sufficient to cover food; hotel with wireless internet would be beneficial so both participants can access the internet at the same time still waiting on travel reimbursement eventhough N ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. Great organizers - very helpful and approachable be clearer about importance and availability of MatLab Wonderful Job! During the final week we were working on our projects we gave progress reports eve ...

Number of daily responses

Page 16 of 16

IAS/PCMI Research Summer School 2010: Image Processing June 27, 2010 to July 17, 2010 IAS/Park City Mathematics Institute, Salt Lake City, UT, USA

Organizers: Tony Chan (University of California, Los Angeles) Ron Devore (University of South Carolina, Columbia) Stanley Osher (University of California, Los Angeles) and Hongkai Zhao (University of California, Irvine)

IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Institute for Advanced Study/Park City Mathematics Institute (PCMI)

2010 Annual Report

The IAS/Park City Mathematics Institute (PCMI) is a program of professional development for the mathematics community, including research mathematicians, graduate students, undergraduate students, mathematics education researchers, undergraduate faculty, and mathematics teachers at the secondary school level. PCMI has been an outreach program of the Institute for Advanced Study since 1994.

The flagship activity of PCMI is the three-week residential Summer Session, held annually in Park City, Utah, a program that combines high-quality lectures/seminars with activities and events designed to foster all-institute interaction. This interaction serves to increase awareness of the roles of professionals in all mathematics-based occupations and creates a strong sense of community.

In addition to the annual Summer Session, PCMI offers year-round professional development activities to secondary school mathematics teachers through its Math Science Partnership project or in the many Professional Development and Outreach Groups.

The Graduate Summer School lectures are typically disseminated through the Park City Mathematics Series of lecture notes, a series targeted at graduate students and researchers, published by the American Mathematical Society. Also published by the AMS is a series of lectures from PCMI’s Undergraduate Summer School. The Math Forum publishes online the products created by PCMI’s Secondary School Teachers Program, and the proceedings and briefs authored by PCMI’s International Seminar on Mathematics Education are also available on the Math Forum website.

Page 2 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Contents Institute for Advanced Study/Park City Mathematics Institute (PCMI) ...... 1 2010 Annual Report ...... 1 The Summer Session ...... 3 Graduate Summer School and Research Program ...... 3 Research Program: ...... 4 Clay Senior Scholar-in-Residence Program ...... 5 Secondary School Teacher Program ...... 6 Undergraduate Summer School ...... 8 Undergraduate Faculty Program ...... 9 International Seminar on Math Education ...... 9 Service, Teaching and Research (STaR) for Early Career Mathematics Educators Project ...... 10 Community and Cross Program Activity: ...... 11 Publication Series ...... 12

IAS/Park City Mathematics Institute governance and management: ...... 13

Page 3 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

The Summer Session

The 20th annual Summer Session, held June 27-July 18, 2010, in Park City, Utah, attracted some 360 participants combined in all programs.

The following programs took place during the Summer Session: • Graduate Summer School • International Seminar on Mathematics Education (one week) • Research Program in Mathematics • Secondary School Teachers Program • Service, Teaching and Research (STaR) Program (one week) • Undergraduate Faculty Program • Undergraduate Summer School

Except as noted, all programs met for the entire three weeks.

The mathematical topic informs the courses and seminars for the Graduate Summer School, the Research Program, the Undergraduate Summer School, and the Undergraduate Faculty Program; in 2010 the topic was The Mathematics of Image Processing. The topic Making Mathematical Connections provided the focus for the International Seminar and the Secondary School Teachers Program.

Each of the programs met daily for a series of courses and seminars. The groups also met together for Cross Program Activities three or four days each week.

Opening social events were held for each program on the evening of Registration Day, designed to introduce participants to their program’s leaders in a casual setting and to foster early acquaintances among the diverse population of each program.

Graduate Summer School and Research Program

The Graduate Summer School and the Research Program 2010 were organized by Professors Tony Chan, Hong Kong University of Science and Technology; Ronald Devore, Texas A&M University; Stanley Osher, University of California Los Angeles; and Hongkai Zhao, University of California Irvine. This year's theme, TheMathematics of Image Processing, included recent developments in mathematical theory, numerical algorithms and applications in image processing. In particular the graduate lecture series and research seminars covered a wide range of topics, such as sparse representations, compressive sensing, image compression, denoising, segmentation, learning and recognition. There were many interactions among participants which are expected to lead to collaborations in the near future.

Page 4 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Graduate Summer School The 2010 Graduate Summer School had nine lecture series on a variety of subjects in image processing and related topics that included sparse coding, compressive sensing, variational and partial differential equation based methods, wavelet, feature learning and optimization. Each lecture series was supplemented with a computer lab, where students got hands-on experience with the lecture material.

Most of the 80 participants in the Graduate Summer School felt that the lectures were well prepared and were well-balanced between introductory and advanced research material and that they benefited a great deal from both the lectures and the lab sessions. The summer program provided graduate students with a comprehensive and diverse learning experience that few, if any, could obtain in their own university.

Graduate Summer School Lecture Series Richard Baraniuk, Rice University: Compressive Sensing: Sparsity-Based Signal Acquisition and Processing Antonin Chambolle, École Polytechnique: Total-Variation based image reconstruction Michael Elad, Israel Institute of Technology: Sparse & Redundant Representations – From Theory to Applications in Image Processing Anna Gilbert, University of Michigan: A survey of sparse approximation Yann LeCun, New York University: Learning Image Feature Zuowei Shen, National University of Singapore: Wavelet and Wavelet Frames in Imaging Science Joseph M. Teran, University of California, Los Angeles: Numerical Methods for Elasticity Problems in Biomechanics Ross Whitaker, University of Utah: Statistical Models and Methods in Image Analysis

Research Program:

There were 35 participants in the Research Program, which consisted mainly of two daily research seminar talks by participants. The speakers list was well balanced between senior and junior researchers. Research talks presented state of the art research and stimulated not only interesting discussions among participants but also possible future collaborations.

Research Program Seminars: Patrick Guidotti, University of California, Irvine: The use of fractional derivatives as an edge detector.

Ernie Esser, University of California, Irvine: A Convex Model for Image Registration Andrea Bertozzi, University of California, Los Angeles: Geometric methods in image processing

Page 5 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Peg Howland, Utah State University: Using Generalized Discriminant Analysis and Factor Analysis Approximations in Dimension Reduction Bin Dong, University of California, San Diego: Some Mathematical Models in Biomedical Shape Processing and Analysis Neus Sabater, Ecole Normale Supérieure de Cachan: Reliability and accuracy in stereovision Marco F. Duarte, Princeton University: Imaging Architectures for Compressive Sensing Jingyue Wang, the University of Georgia: Error bounds for finite-difference methods for Rudin-- Osher--Fatemi image smoothing Xiaoqun Zhang, University of California, Los Angeles: Sparse Reconstruction by Primal-Dual Methods Matthew Herman, University of California, Los Angeles: Grid-Free Denoising of Point-Cloud Data via Non-Local Regularization Xue-Cheng Tai, University of Bergen, Norway and Nanyang Technological University Singapore: Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach Ingrid Daubechies, Princeton University and Duke University: Comparing 2D surfaces in three dimensions, with applications Rick Chartrand, Los Alamos National Laboratory: Nonconvex Compressive Sensing Jian-feng Cai, University of California, Los Angeles: Singular value thresholding algorithms for low-rank matrix completion Karol Gregor, New York University: Learning invariance for deep architectures. Kangyu (Connie) Ni, Arizona State University: Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences Jack Xin, University of California Irvine: Hyperspectral Imaging, Blind Demixing and Fast Optimization Method Jean-Michel Morel, Ecole Normale Supérieure de Cachan, France: ASIFT -- A New Framework for Fully Affine Invariant Image Comparison

Clay Senior Scholar-in-Residence Program

The participation of Professors Daubechies and Morel played a crucial role in the summer program. Each of them gave a very well-received public lecture to the entire PCMI program as well as contributing excellent research seminars. Each Scholar also volunteered to hold a one- hour conversation with the Undergraduate Summer School program: Daubechies spoke about life as a mathematician and Morel spoke about what to expect when doing graduate research in image processing. Very positive feedback on both sessions was given by the undergraduate students. Daubechies’ additional interaction with the Secondary School Teachers Program was very much appreciated by those participants: she attended the SSTP mathematics course, held

Page 6 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

a special session for the SSTP about her work, took part in the Zome building activities and in general made herself available to SSTP participants.

The public lectures given by the Clay Senior Scholars were as follows:

Ingrid Daubechies, Princeton University and Duke University: Fine Art Meets Mathematics Jean-Michel Morel, Ecole Normale Supérieure de Cachan, France: Image editing with the Poisson equation: How to teach the Fourier method to undergraduates

Fifty-two middle school and high school teachers spent three weeks learning mathematics, reflecting on what it means to teach mathematics, and working together to create a product to share with their colleagues both at PCMI and more broadly through the PCMI website.

Of the teacher participants, 16 had returned for a second or third year of participation in the SSTP; four were teachers from the Noyce supplement to the PD3 project; the other participants represented PCMI’s Professional Development and Outreach groups from California, Washington, New Jersey, Utah, and Minnesota including 20 from Mathematics for American in New York City. The remaining teachers came as individuals from a variety of geographic locations such as Arkansas, Florida, Ohio, Maryland and Turkey. The range of teaching experience among the SSTP participants ran from one year of teaching to seasoned veterans.

As in the past nine years, this year’s mathematics session, Developing Mathematics: Over and Over, used materials created by a team led by Al Cuoco and Bowen Kerins from the Educational Development Center (EDC) and the PROMYS for Teachers program at Boston University. Participants explored how iterative processes can be used to investigate Fibonacci numbers, image processing, the calculation of square roots, and more, giving them a useful toolkit of techniques that can be applied to many different areas. Instructors for the course were Darryl Yong from Harvey Mudd College and Bowen Kerins, who is a former teacher and mathematics educator himself.

In the daily Reflecting on Practice session participants considered how to manage productive discussions in their classrooms that contribute to student learning. The time for the course was increased by 15 minutes in response to the concerns raised by the 2009 participant evaluations. The staff of six teachers designed and led the sessions under the guidance and supervision of the SSTP leadership team (Burrill, Hattan and King). Videos of classrooms from the US and other countries, transcripts, research findings, articles, state assessment results and instructional materials were used to prompt an analysis of what constitutes "math talk" and how to create classrooms where the level of discussion and interactivity was at the highest level.

Page 7 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

For two hours each afternoon, participants took part in one of six Working Groups on data analysis, functions, geometry, discrete mathematics, lesson study, and a group that took part in the introductory mathematics course of PCMI’s Undergraduate Summer School (“An Introduction to Mathematical Image Processing,” taught by Professor Luminita Vese of UCLA). In the latter working group, participants not only learned about the 2010 PCMI research topic but adapted it to the secondary classroom with several activities. The other working groups explored technology, developed lessons, classroom activities, and created drafts of potential articles on interesting and useful mathematics that will be tested in classrooms when appropriate, reviewed during the coming year, revised as necessary, and posted on the PCMI website.

Although the Math Science Partnership project, known as PD3, is officially ended, a supplement received from the NSF has continued to support six teachers in New Mexico, five teachers in Seattle and four teachers in McAllen. These teachers were involved in the SSTP in a variety of ways. Two of the McAllen teachers attended SSTP, one of whom was on the staff. Under the leadership of these teachers, seven New Mexico teachers took part in the two morning courses through video conferencing. In addition, three teachers attended SSTP, with one serving as a table leader and as an assistant in the Lesson Study Working Group. The Seattle teachers and some of their colleagues (funded in collaboration with a Carnegie Grant to Seattle Public Schools) attended the first week of the summer Institute, where they took part in the Reflecting on Practice course and spent the rest of the time working as a group to produce a Video Casebook using clips from their own teaching. The Casebook will provide publicly available video classroom examples of important concepts from Complex Instruction that can be shared widely and be used in a variety of professional development settings. The group gave a panel presentation for the SSTP that was very well received.

Overall the summer was very successful, with high ratings from the participants on nearly every element of the program. On a scale of 1 to 4, with 4 as high the goal of learning mathematics received a 3.6 and the math course itself 3.8; reflecting on teaching practice a 3.5 and the course itself a 3.0; becoming a resource for colleagues, 3.5, and the working groups 3.1. A session offered by Darryl Yong, Harvey Mudd College on his year as a high school mathematics teacher in LA was mentioned as a valuable experience. Cross programs received a 2.8 and interaction with the larger community a 3.2. Participants particularly liked pizza and problem solving sessions and appreciated the interaction with Ingrid Daubechies, one of the Clay Scholars, who attended the SSTP mathematics course, held a special session on her work for the SSTP, took part in the Zome building activities and in general made herself available to SSTP participants. Under the direction of Peg Cagle, staff member and middle school teacher from Los Angeles, participants from all of the programs as well as members of the Steering Committee took part in building a giant 4D Zome polytope (photos online at mathforum.org/pcmi/hstp/sum2010/afternoon/peg.html). Another highlight was an informal dinner with the participants from the International Seminar, where those present shared experiences about teaching in different cultures.

Page 8 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

A new feature related to SSTP is the use of Ning, Facebook, and other social networking media by participants. This has provided some real time reflection on the work at SSTP and gives us an opportunity to see what things are making a difference for the participants. A post summer institute blog is attached below as an example of the effect of SSTP on one participant.

Undergraduate Summer School

The 2010 Undergraduate Summer School (USS) at PCMI was, as customary, organized around a pair of courses taught each day with daily problem sessions; one course was primarily aimed at introductory level students (and a group of motivated high school teachers) and the other was intended for students at a more advanced undergraduate level of mathematics. The introductory course was An Introduction to Mathematical Image Processing, taught by Professor Luminita Vese of UCLA, and the advanced course was An Introduction to Compressed Sensing, taught by Professor Jared Tanner of the University of Edinburgh.

Both courses were accessible to the students and received generally positive reviews. Attendance was high throughout the three week session, filling the room to capacity (about 40- 50 students). In addition, because of the topic, the daily problem sessions (conducted by Jeff Blanchard of Grinnell College and Todd Wittman of UCLA) included crucial programming components. These problem sessions were remarkably popular with the students.

Professor Vese’s introductory course covered techniques for image filtering using first- and second-order partial derivatives, the gradient, Laplacian, and their discrete approximations by finite differences, average filters, convolution operators, the Fourier transform, low-pass and high-pass filters. It was presented at a level that was easy for student to understand and implement in the lab.

In keeping with PCMI's focus on cross-program participation, a group of secondary mathematics teachers led by Professor James King of the University of Washington created a working group on Image Processing and attended two weeks of the Professor Vese’s lectures. This group created a handful of exercises center around simple image processing transformation that could be taught to secondary students.

Professor Tanner’s advanced course discussed Fourier series and wavelets, before delving into selected topics in compressed sensing. It was remarkable to see that many of his lectures were also independently covered in the graduate summer school. Usually the gap between the advanced undergraduate course and graduate courses is immense. This year it was almost non- existent, probably due to the newness of the field.

The applicant pool this year was on the small side (approximately 60 applicants for 40 slots), probably due to the fact that PCMI is less well known in the applied math/engineering communities. Nevertheless, the students who attended seemed well prepared and reported a high level of satisfaction with the program.

Page 9 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Undergraduate Faculty Program

For faculty members whose main focus is teaching undergraduate students, the Undergraduate Faculty Program (UFP) at PCMI offers the opportunity to renew excitement about mathematics, talk with peers about new teaching approaches, address some challenging research questions, and interact with the broader mathematical community. The UFP is unique in that it bridges the educational and research objectives of PCMI.

This year's UFP instructor/coordinator was Professor Kevin Vixie, who was assisted by Professor Tom Asaki (both at the Washington State University). The UFP had three threads this year:

1. Metrics and Regularization in Image Processing: This set of 15 lectures by Professor Vixie introduced the topic of image metrics and regularization and their role in image processing.

2. Data Challenges and Algorithms: Professor Asaki grouped the participants in teams and had them explore concrete image processing problems using MATLAB. The participants learned how to implement the algorithms described in the primary lecture series. The problems were set as challenges, with some good-natured competition between the individual teams.

3. Lectures on Geometric Measure Theory: Professor Asaki presented a set of 6 advanced lectures discussing Geometric Measure Theory and its relation to image processing. The lectures attracted graduate students and members of the research program in addition to many of the UFP participants.

The UFP was unusually popular this year, attracting 22 participants. The group was enthusiastic about working on the data challenges in a team setting; many participants felt that acquiring a familiarity with image processing would help them with their own research and/or could be incorporated into courses at their home institution.

International Seminar on Math Education

Page 10 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

of their own cultures. Michèle Artigue, Past President of the International Congress on Mathematical Instruction, was co-leader with Gail Burrill, Past President of the National Council of Teachers of Mathematics. Herb Clemens was a responder to presentations. Johnny Lott, Past President of the National Council of Teachers of Mathematics served as an organizer with Gail Burrill to set up the seminar.

Issues emerging from the conversations formed the basis for jointly written policy briefs on topics of mutual concern. The 2010 briefs deal with the what, how and why of the use of the concepts in classrooms and in teacher preparation. Once edited, these briefs will appear with the previous policy briefs and the proceedings of the earlier seminars on PCMI’s web site at the Math Forum, http://mathforum.org/pcmi/int.html. The Seminar received excellent reviews from the participants, who commented on the social networking opportunities and intellectual stimulation of the program.

Service, Teaching and Research (STaR) for Early Career Mathematics Educators Project

New this year to PCMI was the STaR workshop for recent doctoral graduates in mathematics education. This one-week program was organized by Professors Robert Reys and Barbara Reys from the University of Missouri, with NSF funding.

The goals of the project are to bring together a cadre of future leaders of mathematics education in order to: • Establish a support structure for advancing the scholarship of recent doctoral graduates in mathematics education; • Expand the networking of recent graduates/advanced graduate students initiated by CLTs to graduates/advanced graduate students from other institutions; • Showcase research priorities for the field and facilitate the establishment and development of research groups involving young mathematics education scholars from different institutions.

The 44 STaR Fellows of 2010 have appointments in 42 different institutions throughout the U.S. Twenty-four Fellows have appointments in mathematics departments and 20 in colleges/departments of education. Outstanding scholars were recruited to lead or facilitate sessions. Professor Jere Confrey, North Carolina State University; Professor James Hiebert, University of Delaware; and Professor Denise Mewborn, University of Georgia made keynote presentations and worked with the STaR Fellows in follow-up breakout sessions. Dr. John (Spud) Bradley of the National Science Foundation also attended the Institute for several days and interacted with attendees.

Page 11 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Community and Cross Program Activity:

Efforts toward building a strong and dynamic community among all PCMI participants included the use this year of a social networking site known as Ning.com, which was successful at encouraging communication among all participants in a variety of ways. PCMI’s Ning site included discussions, posting of events and schedules, notices of activities organized by participants, blog posts, and an individual and customizable page for each participant. Out of the 364 participants at PCMI this year, some 275 participated in the Ning community. PCMI’s Ning site also included group pages for each program (Graduate Summer School, Undergraduate Summer School, etc.) and sub-programs (e.g. the Working Groups of the Secondary School Teachers Program). Following PCMI’s policy of opening all programs to all participants, the participants were free to join any Ning group that they wished to follow. Most of the online groups were used quite extensively for the posting of discussions, activities, schedule notices and lecture notes. Less noticeable were personal status updates or personal comments from individuals.

Community is also built at PCMI through a variety of Cross Program Activities – a mix of formal presentations and informal recreational activities.

Formal: • Clay Senior Scholars-in-Residence lectures by Jean-Michel Morel and Ingrid Daubechies • Presentation by Tony DeRose, Pixar Animation Studios • Presentation by Nick Jackiw, Key Curriculum Press • Pizza and Problem Solving sessions (2) were held, organized by Andrew Bernoff, Harvey Mudd College. • Opening Socials were held for each program on the opening day of PCMI. • Opening and Closing Dinners were held on the first Monday and last Thursday. • Informal: • Designing and building the customary 4th of July Parade entry (a hypercube to represent this year’s parade theme “From Silver to Snow”). Some 60 people participated in the parade activities. • The Director’s Hike. Organized by Director Richard Hain, this activity took place on a Wednesday afternoon, with 25 (self-selected) participants from among the programs. • The PCMI World Cup Soccer Match. 34 players of varying skill levels participated, with about 50 people as spectators. • The annual Ice Cream Social was organized and hosted by the participants of the Secondary School Teachers Program. Construction activities were available throughout the evening.

Participants are encouraged to organize sports and recreational outings, which was done via notices posted on the bulletin board located in the conference center or in the Ning online community. After the first week, there were participant-led sports activities held nearly every

Page 12 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

night and on the weekends, as well as weekend trips organized and open to anyone who wished to go.

The Opening Socials, held on the first Sunday evening of PCMI were a big success, affording the participants an opportunity to meet each other and their lecturers and organizers before beginning seminars and courses together for three weeks.

Publication Series Published by the American Mathematical Society, the Park City Mathematics Series comprises nearly all of the lectures ever given in PCMI’s Graduate Summer School.

Also published are six volumes in the Park City Mathematics Institute Subseries, a subsection of the AMS Student Mathematics Series. These volumes are aimed at undergraduate students and are published independently of the Park City Mathematics Series .

The Secondary School Teachers Program disseminates its teacher-created materials and other resources via a special website created by the Math Forum at Drexel University. Challenges have been encountered with the publication of this material during a transition year (Professor Johnny Lott stepped down as editor in 2009). Professor Emeritus Bob Stein (California State University San Bernadino), has agreed to assume the role on a trial basis starting in the Fall of 2010.

A full list of PCMI’s publications is included in the Annual Report available at http://pcmi.ias.edu.

Funding The IAS/Park City Mathematics Institute was made possible by the generosity of the following funders:

• The National Science Foundation, grants: EHR-0314808, DMS-0940733, and EHR-0554309 • Eric and Wendy Schmidt • Math for America • The National Security Agency • Charles and Rosanna Jaffin • The George S. and Dolores Doré Eccles Foundation • The Wolfensohn Family Foundation • The Clay Mathematics Institute • The Mathematical Sciences Research Institute

Appreciation is extended for the in-kind contributions of the Department of Mathematics at the University of Utah.

Page 13 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

IAS/Park City Mathematics Institute governance and management

Deborah Ball, University of Michigan Hyman Bass, University of Michigan Peter Goddard, Institute for Advanced Study Ronald Graham, University of California San Diego Robert MacPherson, Institute for Advanced Study Elaine Wolfensohn, Wolfensohn Family Foundation

PCMI Steering Committee 2010:

Director: Richard Hain, Duke University

Aaron Bertram, University of Utah Andrew J. Bernoff, Harvey Mudd College Gail Burrill, Michigan State University Tony F. Chan, University of California-Los Angeles Ronald A. DeVore, University of South Carolina-Columbia Carol Hattan, Skyview High School, Vancouver, WA Helmut Hofer, Institute for Advanced Study James King, Universtiy of Washington Johnny Lott, University of Mississippi Janis Oldham, North Carolina Agriculture and Technical State University John Polking, Rice University Ronald Stern, University of California-Irvine Karen Vogtmann, Cornell University Hongkai Zhao, University of California-Irvine

PCMI Diversity Sub-Committee:

Chair: Janis Oldham, North Carolina Agriculture and Technical State University

Erika Camacho, Arizona State University Duane Cooper, Morehouse College Edray Goins, Purdue University Leona Harris, The College of New Jersey Robert Megginson, University of Michigan Robin Wilson, Cal Poly Pomona

Page 14 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Invited Participants

firstname lastname institutionname Stuart Ambler University of Notre Dame Natth Bejraburnin University of California, Berkeley Reuben Brasher University of California, Berkeley Susanna Dann Louisiana State University Matthew Elsey University of Michigan Jung Eun Korea Advanced Institute of Science and Technology (KAIST) Christina Frederick University of Texas Jarod Hart University of Kansas Qianying Hong University of Georgia Xiang Huang University of Connecticut John Jasper University of Oregon Dain Jeong Korea Advanced Institute of Science and Technology (KAIST) Myeong Min Kang Seoul National University Qin Li Florida State University Wenjing Liao University of California, Berkeley Leopold Messi University of Georgia Sharad Silwal Kansas State University Daniel Wang University of Oregon Xun Wang Michigan State University Ke Yin Georgia Institute of Technology

Page 15 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Invited Participants Participants 20

Gender 20 Male 65.00% 13 Female 35.00% 7 Declined to state 0.00% 0

Ethnicity* 21 White 28.57% 6 Asian 61.90% 13 Hispanic 0.00% 0 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 9.52% 2 * ethnicity specifications are not exclusive

Page 16 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 11 100% partially 0 0% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? above satisfactory 3 27% satisfactory 8 73% not satisfactory 0 0% no opinion 0 0%

Was there too much material presented; was the workshop too ambitious?

Page 18 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City too much 3 27% just right 7 64% not enough 1 9% no opinion 0 0%

Was the problem session helpful? yes 5 45% partially 5 45% no 1 9% no opinion 0 0%

Additional comments on the topic presentation and organization Coherent - one wouldn't want something too tidy; in fact there was more redundancy, people talking on the same topic, than I might have liked. Too much material - yes, many speakers fell prey to th ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 8 73% partially 3 27% no 0 0%

Page 19 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City Did the workshop increase your interest in the subject? yes 10 91% partially 1 9% no 0 0%

Was the workshop worth your time and effort? yes 10 91% partially 1 9% no 0 0%

Is it likely that you will work in the area of the workshop subject in the future? yes 8 73% partially 3 27% no 0 0%

How would you evaluate your interaction with other participants?

Page 20 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City 1 - above satisfactory 3 27% 2 5 45% 3 3 27% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Page 21 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City

Additional comments on your personal assessment It was a little noisy in the lunch tent for entirely comfortable conversation for me. Also I would have liked more formal interaction with people in other groups.

Venue

Please rate the different categories

Your overall experience 1 - above satisfactory 6 55% 2 4 36% 3 1 9% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The assistance provided by staff 1 - above satisfactory 9 82% 2 1 9% 3 1 9% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The physical surroundings

Page 22 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City 1 - above satisfactory 8 73% 2 3 27% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on the venue great location

Accommodation and Food

Please rate the different categories

The summer school accommodation 1 - above satisfactory 5 45% 2 2 18% 3 3 27% 4 1 9% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The food provided

Page 23 of 24 IAS/PCMI Research Summer School 2010: Image Processing, June 27, 2010 to July 17, 2010 at the IAS/Park City Mathematics Institute, Salt Lake City 1 - above satisfactory 2 18% 2 7 64% 3 0 0% 4 2 18% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on accommodation and food The food was unimaginative institutional food, but I never went hungry. The vegetarian option was handled well except there didn't seem to be much attention to providing adequate well balanced prot ...

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. I'm very grateful that I came.

Number of daily responses

Page 24 of 24

Algebraic, Geometric, and Combinatorial Methods for Optimization August 2, 2010 to August 13, 2010 MSRI, Berkeley, CA, USA

Organizers: Matthias Köppe (University of California, Davis) Jiawang Nie (University of California, San Diego)

Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

MSRI Summer Graduate Workshop Algebraic, Geometric, and Combinatorial Methods for Optimization

Matthias K¨oppe (University of California, Davis) Jiawang Nie (University of California, San Diego) August 2010

The goal of this summer graduate workshop was to introduce students to the very recent exciting developments in both continuous and discrete optimization, using algebraic, geometric, and combinatorial methods. None of these recent developments are typically covered, as of yet, in graduate optimization courses. The structure of the workshop was as follows.

1. Two lecture series on continuous optimization, of 7 lectures each, in the first week. Jiawang Nie (University of California, San Diego) introduces the basic theory of semidefinite programming, which includes convex sets and linear matrix inequalities, duality theory, optimality conditions, and applications such as in control and optimization. Complementary to that, Greg Blekherman (Virginia Tech) introduced positive polynomials, sum of squares, basic real algebraic geometry, and its connections to semidefinite programming, including applications and software. 2. Two lecture series on discrete optimization, of 7 lectures each, in the second week. Shmuel Onn (Technion – Israel Institute of Technol- ogy) introduced Graver basis methods in nonlinear discrete optimization. Matthias Köppe presented rational generating function techniques in integer programming and the necessary prerequisites in the geometry of numbers. 3. Problem sessions, on each afternoon, were led by the teaching assistants Amitabh Basu and Cynthia Vinzant. The students were divided into small groups, who met in separate locations in MSRI to work together on subsets of the problems each. At the end of the afternoon, students presented their results in the auditorium. 4. Evening sessions, after dinner in the dorms, were held on several days by lecturer Greg Blekherman and teaching assistant Amitabh Basu. Part of the time was used to discuss further some of the problems worked on

Page 2 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

in the afternoon. Another part was used to introduce, to those students interested, basic material such as on computational complexity and on polyhedral convexity.

Details on the lecture series Jiawang Nie: Semidefinite programming (7 lectures) This lecture series was presenting basic and new research results of solving general polynomial optimization via semidefinite programming and sum of squares techniques. Its aim was to help students understand the properties, both mathematical and computational, of semidefinite programming, sum of squares, polynomial optimization, and their applications. In particular, we worked towards methods that will enable the solution of optimization problems with feasible sets that are defined through polynomial systems. There is a very interesting interaction between algebraic geometry and convex optimization. Two basic semidefinite programming relaxation methods: Lasserre type and Jacobian type SDP relaxations are concentrated in the lectures. In addition to the theoretical sides, the students were also trained to use the software like GloptiPoly, SOSTOOLS, YALMIP, SeDuMi, which are frequently used in the area.

Greg Blekherman: Positive polynomials and sums of squares (7 lectures) This lecture series presented the basic theory of nonnegative (psd) and sum of squares (sos) polynomials. The question of relationship between psd and sos polynomials has been receiving renewed attention because it was realized that the question of testing whether a polynomial is sos is actually computationally tractable and it can be solved via semideﬁnite programming. This subject to related the famous Hilbert’s 17-th problem: is every nonnegative polynomial a sum of squares of rational functions? Hilbert characterized when nonnegative polynomials are sos, and proved the existence of nonnegative polynomials that are not sos. Hilbert’s 17-th problem is solved aﬃrmatively, and brought a new area of real algebra. The basic theory and applications in real algebra were presented in this lecture series.

Shmuel Onn: Graver basis methods in nonlinear discrete optimization (7 lectures) This lecture series was presenting an algorithmic theory of nonlinear discrete optimization. It introduced a simple and useful setup which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of

Page 3 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

Graver bases. The power of the theory was demonstrated by deriving the ﬁrst polynomial time algorithms in a variety of application areas.

Matthias Köppe: Geometry of numbers and rational generating function techniques in integer programming (7 lectures) This lecture series was on rational generating function techniques for integer programming. Starting with Barvinok’s pioneering 1994 work on short rational generating functions for integer points in polyhedra of fixed dimension, generating function techniques have entered the world of discrete optimization. The techniques lead to efficient algorithms for important problem classes such as mixed-integer polynomial optimization over polytopes, which are unmatched by other methods. The lectures first discussed the complexity status of integer optimization problems and then introduced tools from the geometry of numbers such as Minkowski’s theorem, Khinchin’s flatness theorem, and shortest vector algorithms, with a detour to Lenstra’s algorithm for integer programming in fixed dimension. This was followed by geometric decomposition results, including the Gram–Brianchon theorem, Barvinok’s signed decomposition, and results on triangulations and half-open decompositions. Then the valuative theory of rational generating functions in the form of the Lawrence–Pukhlikov–Khovanskii and Brion theorems and Barvinok’s polynomial time lattice-point counting algorithm (in fixed dimension) were introduced. After completing this theory, the lectures showed the applications in integer programming, in particular the algorithms based on the summation method for polynomial integer programming. The final lecture gave an overview over some advanced results in optimization using the Barvinok–Woods integer projection theorem.

Conclusion

Both organizers felt that the organization of the workshop went very well, and that it has provided a great learning experience to most of the graduate participants.

Page 4 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

Speaker/Organizer firstname lastname institutionname Grigoriy Blekherman University of Michigan Matthias Koeppe University of California, Berkeley Jiawang Nie University of California, San Diego Shmuel Onn Technion---Israel Institute of Technology

Teaching Assistant firstname lastname institutionname Amitabh Basu University of California, Davis Cynthia Vinzant University of California, Berkeley

Page 5 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

MSRI Summer Graduate Workshop: Algebraic, Geometric, and Combinatorial Methods for Optimization Schedule of Week # 1

Time \ Date August 2 August 3 August 4 August 5 August 6

09:30-10:30 Nie Blekherman Nie Nie Blekherman

10:30-11:00 Tea Break Tea Break Tea Break Tea Break Tea Break

11:00-12:00 Blekherman Nie Blekherman Blekherman Nie

12:00-02:00 Lunch Lunch Lunch Lunch Lunch

02:00-03:00 Nie Blekherman Open Nie Blekherman

03:00-xy:zw Discussion Discussion Open Discussion Discussion

Page 6 of 16 Algebraic, Geometric, and Combinatorial Methods forOptimization,August2,2010to13,atMSRI,Berkeley Geometric, andCombinatorial Algebraic, MSRI Summer Graduate Workshop: Algebraic, Geometric, and Combinatorial Methods for Optimization Schedule of Week # 2

Monday Tuesday Wednesday Thursday Friday Lecture: Lecture: Lecture: Lecture: Lecture: 09:30 - 10:00 AM Shmuel Onn Matthias Köppe Shmuel Onn Matthias Köppe Matthias Köppe 10:30 - 11:00 AM Tea Tea Tea Tea Tea Lecture: Lecture: Lecture: Lecture: Lecture: 11:00 - 12:00 PM Matthias Köppe Shmuel Onn Matthias Köppe Shmuel Onn Shmuel Onn

Page 7of 16 12:00 - 02:00 PM Lunch Lunch Lunch Lunch Lunch Lecture: Lecture: Lecture: Lecture: 02:00 - 03:00 PM Shmuel Onn Matthias Köppe Shmuel Onn Matthias Köppe 03:00 - 03:30 PM Tea Tea Tea Tea Recitations: Recitations: Recitations: Recitations: 03:30 - 05:00 PM Amitabh Basu Amitabh Basu Amitabh Basu Amitabh Basu Dinner Dinner Dinner Dinner End of Workshop 05:00 - 07:00 PM Location: Dorms Location: Dorms Location: Dorms Location: Dorms Supplementary Supplementary Supplementary Recitation/Tutorial: Recitation/Tutorial: Recitation/Tutorial: 07:00 PM - Open Amitabh Basu Amitabh Basu Amitabh Basu Location: Dorms Location: Dorms Location: Dorms

Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

Invited Participants firstname lastname institutionname Ahmad Alzaghal Central Michigan University Yan Cheng Baylor University Justin DeVries University of Nebraska Hongbo Dong University of Iowa Dmitriy Drusvyatskiy Cornell University Andri Egilsson Reykjavik University Tom Fielden Portland State University Patricio Gallardo SUNY Gamze Gursov University of Illinois, Chicago Nathan Hamlin Washington State University Bradley Hannigan-Daley University of Toronto Marteinn Hardarson Reykjavik University Nancy Ho University of Oklahoma Sheng Huang University of Hong Kong Jiwoon Kim Seoul National University Christine Klymko Emory University Alexander Levin Massachusetts Institute of Technology Qinghua Luo University of Oklahoma Casey Monday University of Kentucky Kenneth Monks Colorado State University Jennifer Park Massachusetts Institute of Technology Pei Pei Universtiy of Prince Edward Island James Pfeiffer University of Washington Anthony Preslicka Georgia State University Uma Ravat University of Illinois Eric Riley Portland State University Yan Shu Georgia Institute of Technology Laura Silverstein San Diego State University Richard Spjut University of California, Berkeley Derrick Stolee University of Nebraska-Lincoln Anastasia Svishcheva Emory University Ngoc Tran University of California, Berkeley Gah-Yi Vahn University of California, Berkeley Ran Wang New Mexico Tech Li Wang University of Oregon

Page 8 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

Officially Registered Participant Information Participants 35

Gender 35 Male 60.00% 21 Female 37.14% 13 Declined to state 2.86% 1

Ethnicity* 35 White 48.57% 17 Asian 40.00% 14 Hispanic 2.86% 1 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 8.57% 3 * ethnicity specifications are not exclusive

Page 9 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

Guests firstname lastname institutionname Natth Bejraburnin University of California, Berkeley Robert Hildebrand University of California, Davis Robert Korsan Decisions, Decisions! Benjamin Lorenz FU Berlin, Institut für Mathematik Caroline Uhler Universtiy of California, Berkeley

Page 10 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley

responses

See complete responses

Topic Presentation and Organization

Did the various topics within the workshop integrate into a coherent picture? yes 15 68% partially 6 27% no 0 0% no opinion 1 5%

Were the speakers generally clear and well organized in their presentation? above satisfactory 12 55% satisfactory 9 41% not satisfactory 1 5% no opinion 0 0%

Was there too much material presented; was the workshop too ambitious?

Page 12 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley too much 4 18% just right 17 77% not enough 1 5% no opinion 0 0%

Was the problem session helpfull? yes 13 59% partially 7 32% no 1 5% no opinion 1 5%

Additional comments on the topic presentation and organization I enjoyed the second week more than the first. The two weeks were individually well-integrated, but did not meet very much. Matthias Koeppe is definitely one of the most clear well-organized presenter ...

Personal Assessment

Was your background adequate to access a reasonable portion of the material? yes 17 77% partially 5 23% no 0 0%

Page 13 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley Did the workshop increase your interest in the subject? yes 17 77% partially 5 23% no 0 0%

Was the workshop worth your time and effort? yes 22 100% partially 0 0% no 0 0%

Is it likely that you will work in the area of the workshop subject in the future? yes 10 45% partially 11 50% no 1 5%

Additional comments on your personal assessment The second week was definitely way more relevant to what I'm doing, so I really enjoyed that. I found the lectures to be very easy, and I wish more materials were presented. I was surprised that a l ...

Venue

Page 14 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley Your overall experience at MSRI 1 - Above satisfactory 13 59% 2 6 27% 3 1 5% 4 0 0% 5 - Not satisfactory 2 9%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff 1 - Above satisfactory 14 64% 2 5 23% 3 2 9% 4 0 0% 5 - Not satisfactory 1 5%

Above satisfactoryNot satisfactory

The overal atmosphere of MSRI 1 - Above satisfactory 17 77% 2 3 14% 3 1 5% 4 0 0% 5 - Not satisfactory 1 5%

Above satisfactoryNot satisfactory

The physical surroundings

Page 15 of 16 Algebraic, Geometric, and Combinatorial Methods for Optimization, August 2, 2010 to August 13, 2010 at MSRI, Berkeley 1 - Above satisfactory 18 82% 2 3 14% 3 0 0% 4 0 0% 5 - Not satisfactory 1 5%

Above satisfactoryNot satisfactory

Additional comments on the venue it would have been nice to have had more consistent access to the patio outside the upper commons The venue was amazing!

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. MSRI itself was awesome but I really really really did not like having the food money only usable at the dorm dining hall. I tried to cash out my meal card so that I could just purchase breakfast o ...

Number of daily responses

Page 16 of 16

Sage Days 22: Computing with Elliptic Curves June 21, 2010 to July 2, 2010 MSRI, Berkeley, CA, USA

Organizers: William Stein (University of Washington)

Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Sage Days 22: Computing with Elliptic Curves Final Report

William Stein March 11, 2011

1 Overview

Sage Days 22 was a graduate student workshop at MSRI in Berkeley, CA from June 21, 2010 to July 02, 2010. In addition to over 50 graduate student attendees, there were numerous more senior mathematicians that delivered lectures and mentored students, including: John Cremona (Warwick), Tim Dokchitser (Cambridge), Noam Elkies (Harvard), Matt Greenberg (Calgary), Ken Ribet (Berkeley), William Stein (University of Washington), Jared Weinstein (UCLA), Christian Wuthrich (Nottingham), Robert Miller (University of Washington), and Robert Bradshaw (Google). Most days of the workshop started with student status reports, followed by 3 or 4 talks about mathematics, and an afternoon of working sessions. On the ﬁrst Friday, we organized a special day devoted to open source research computation, which included two speakers from Google, two speakers from the Neuroimagining group at UC Berkeley, and a scientist from India. This gave the student participants a better sense of how the number theoretic computation ﬁts into the broader computational ecosystem.

Tim Dokchitser, one of the project leaders

2 Project Groups

There were ﬁve projects about various aspects of the arithmetic of elliptic curves. Each morning during status reports students would describe what they had

Page 2 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

accomplished toward their projects. The style was a bit like the Arizona Winter School (which Stein has been heavily involved with), but with fewer students and two weeks instead of one, which allowed students to spend much more time on projects. Also, there was a strong focus on software, and many more opportunities for students to report to everybody what they were working on, which dramatically increased collaboration. Every project involved substantial research level mathematics. Many projects resulted in substantial code contributions to Sage (http://sagemath.org), and projects started at the workshop have in some cases continued for months af- terwards. Each lecture series corresponded to one of the project groups. In addition, Ken Ribet gave a colloquium on Galois representations, since they are a common theme in all of the projects, and Noam Elkies gave a talk full of clever observations he made related to some of the projects.

2.1 The ﬁve project groups 1. John Cremona (Warwick University, UK): Tables of elliptic curves 2. Tim Dokchitser (Cambridge University, UK): Complex L-functions and the Birch and Swinnerton-Dyer conjecture 3. Matthew Greenberg (University of Calgary): Mod p representations associated to elliptic curves 4. Jared Weinstein (UCLA) and William Stein (University of Washington): Heegner Points and Kolyvagin’s Euler system 5. Christian Wuthrich (Nottingham University, UK): p-adic L-series and Iwasawa theory For technical details about exactly what each project consisted of, see http://wiki.sagemath.org/days22.

3 Final Presentations

The last day of the workshop was devoted to student presentations, in which every group presented the results of nearly two weeks of very exciting work.

Page 3 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Lecturers

firstname lastname institutionname John Cremona University of Warwick Tim Dokchitser University of Cambridge Matthew Greenberg University of Calgary Jared Weinstein University of California Christian Wuthrich School of Mathematical Sciences William Stein University of Washington

Teaching Assistants

firstname lastname institutionname Robert Miller University of Warwick

Guest Speakers

firstname lastname institutionname Robert Bradshaw University of Washington Lloyd Kilford Jarrod Millman UC Berkeley Peter Norvig Google Fernando Perez Henry H. Wheeler, Jr. Brain Imaging Center Prabhu Ramachandran Indian Institute of Technology Kenneth Ribet UC Berkeley

Page 4 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Sage Days 22: MSRI Graduate Student Workshop Schedule

Monday, June 21 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am Ride bus to MSRI 9:00am – 9:30am Arrive at MSRI and sign in 9:30am – 9:45am MSRI director: introduction and orientation 9:45am – 10:00am Stein: Introduction and orientation about this workshop 10:00am – 10:55am Dokchitser: talk 1 11:00am – 11:55am Weinstein: talk 1 12:00pm – 2:00pm Lunch 2:00pm – 2:50pm Greenberg: talk 1 3:00pm – 3:30pm Participant introductions 3:30pm – 4:00pm Tea 4:00pm – 6:10pm Working Sessions 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Tuesday, June 22 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am Ride bus to MSRI 9:00am – 9:30am Stein: Project status reports 9:30am – 10:20am Cremona: talk 1 - Tables of Elliptic Curves 10:30am – 11:20am Greenberg: talk 2 - Arithmetic of p-adic and mod p representations 11:30am – 12:20pm Wuthrich: talk 1 12:20pm – 2:00pm Lunch at MSRI 2:00pm – 6:10pm Working sessions 3:30pm – 4:00pm Tea 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Wednesday, June 23 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am, 9:10am Ride bus to MSRI 9:30am – 10:00am Stein: Project status reports 10:00am – 10:50am Cremona: talk 2 - Verifying optimality and Manin’s conjecture 11:00am – 11:50am Stein: talk 1 - Computing Heegner points in Sage 11:30am – Workshop Barbecue at Willows Picnic Site 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Thursday, June 24 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am, 9:10am Ride bus to MSRI 9:30am – 10:00am Stein: Project status reports 10:00am – 10:50am Cremona: talk 3 - Computing Isogenies 11:00am – 11:50am Cremona: talk 4 - Finding all elliptic curves with good reduction outside a given set of primes 12:00pm – 2:00pm Lunch at MSRI 2:00pm – 6:10pm Working sessions 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Friday, June 25 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am Ride bus to MSRI 09:00am – 09:10am Millman and Stein: Welcome 09:10am – 10:10am Norvig (Google): What to demand from a Scientific Computing Language 10:10am – 11:00am Perez (Berkeley) Python: an ecosystem for scientific computing 11:00am – 11:50am Bradshaw (Google): Cython: the best of both worlds 12:00pm – 2:00pm Lunch 1:00pm – 2:50pm Ramachandran (IIT Bombay): Python in science and engineering education in India 2:50pm – 3:40pm Stein (Univ of Washington): Sage: creating an open source alternative to Ma* 3:40pm – 4:10pm Tea 4:10pm – 5:00pm Millman (Berkeley): The Foundation for mathematical and scientific computing 5:00pm – 6:10pm Discussion 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops

Page 5 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Monday, June 28 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am, 9:10am Ride bus to MSRI 9:30am – 10:00am Stein: Project status reports 10:00am – 10:50am Weinstein: talk 2 11:00am – 11:50am Greenberg: talk 3 12:00pm – 2:00pm Lunch at MSRI 2:00pm – 4:00pm Working sessions 4:00pm – 5:00pm Cremona’s students: presentations 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Tuesday, June 29 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am Ride bus to MSRI 9:00am – 9:30am Stein: Project status reports 9:30am – 10:20am Wuthrich: talk 2 10:30am – 11:20am Weinstein: talk 3 11:30am – 12:20pm Dokchitser: talk 2 12:20pm – 2:00pm Lunch 2:00pm – 6:10pm Working sessions 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Wednesday, June 30 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am Ride bus to MSRI 9:00am – 9:30am Stein: Project status reports 9:30am – 10:20am Wuthrich: talk 3 10:30am – 11:20am Dokchitser: talk 3 11:30am – 12:20pm Ribet: Colloquium on Galois Representations 12:20pm – 2:00pm Lunch at MSRI 2:00pm – 3:00pm Kilford:A Gentle Introduction to Overconvergent Modular Forms 3:00pm – 6:10pm Working sessions 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Thursday, July 1 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am Ride bus to MSRI 9:00am – 9:30am Stein: Project status reports 9:30am – 10:20am Dokchitser: talk 4 10:30am – 11:20am Wuthrich: talk 4 11:30am – 12:20pm Weinstein: talk 4 12:20pm – 2:00pm Lunch at MSRI 2:00pm – 6:10pm Working sessions 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility 7:30pm – 11:30pm Working session at the dorm and/or coffee shops Friday, July 2 7:00am – 8:00am Breakfast at Foothill dining facility 7:40am, 8:10am, 8:40am, 9:10am Ride bus to MSRI 9:30am – 10:20am Dokchitser’s student presentations 10:30am – 11:50pm Greenberg’s student presentations 12:00pm – 2:00pm Lunch at MSRI 2:00pm – 2:50pm Stein/Weinstein’s student presentations 3:00pm – 3:50pm Wuthrich’s student presentations 4:00pm – 4:30pm Cremona students (part 2) 4:55pm, 5:25pm, 5:55pm, 6:25pm, 7:15pm Bus down hill 5:30pm – 7:00pm Dinner at Foothill dining facility

Page 6 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Invited Participants

firstname lastname institutionname David Ai Indiana University Jaquelin Anderson Brown University Lunaho Ao University of Missouri Jennifer Balakrishnan Massachusetts Institute of Technology Rebecca Bellovin Stanford University John Bergdall Brandeis University Erin Beyerstedt Tulane University - Mathematics Dept Shuchau Bi University of California, Berkeley Jon Cass University of California, Berkeley Feng Chen University of California, Berkeley Michael Daub University of California, Berkeley Alyson Deines University of Washington Ding Ding Binghamton University (SUNY) Daniel Disegni Columbia University Indika Gamage Wesleyan University Dario Garcia University of Los Andes Anna Haensch Wesleyan University Mustafa Hajij Louisiana State University Pin-Hung Kao Central Michigan University Rodney Keaton Clemson University Chan-Ho Kim Boston University Ben Linowitz Dartmouth College Michael Lipnowski Stanford University megan Maguire University of California, Santa Barbara Erin Militzer University of Kentucky Khoa Nguyen University of California, Berkeley Laura Peskin California Institute of Technology M.Tip Phaovibul University of Illinois at Urbana-Champaign Vincent Rusnell Clemson University Hatice Sahinoglu Brown University Arijit Sehanobish University of Maryland Gagan sekhon University of Connecticut Adam Sorkin University of California, Berkeley James Stankewicz University of Georgia Armin Straub Tulane University Lauren Thompson Dartmouth College Anil Venkatesh Duke University

Page 7 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

firstname lastname institutionname Jeremy West University of Michigan Ian Whitehead Columbia University Xiao Xiao Binghamton University (SUNY) Donggeon Yhee Seoul National University

Guests

firstname lastname institutionname Barinder Banwait University of Warwick Noam Elkies Harvard University Radoslav Kirov University of Illinois at Urbana-Champaign Geoffrey Lee Harvard University Brandon Levin Stanford University Samuel Lichtenstein Harvard College Chung Pang Mok Harvard University Charlie Turner University of Warwick Justin Walker Stanford University James Weigandt Purdue University

Page 8 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Invited Participants Statistics

Participants 41

Gender 41 Male 68.29% 28 Female 24.39% 10 Declined to state 7.32% 3

Ethnicity* 41 White 56.10% 23 Asian 36.59% 15 Hispanic 2.44% 1 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 4.88% 2 * ethnicity specifications are not exclusive

Page 9 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 30 83% partially 6 17% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? above satisfactory 26 72% satisfactory 10 28% not satisfactory 0 0% no opinion 0 0%

Was there too much material presented; was the workshop too ambitious?

Page 11 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

too much 6 17% just right 29 81% not enough 1 3% no opinion 0 0%

Was the problem session helpfull? yes 26 72% partially 4 11% no 1 3% no opinion 5 14%

Additional comments on the topic presentation and organization great, it would have been nice to have had the talks online too. Tim Dokchitser's lectures were exceptionally clear and well-organized - I really learned a lot from him. Maybe I'm being naive, but I t ...

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 23 64% partially 13 36% no 0 0%

Page 12 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Did the workshop increase your interest in the subject? yes 34 94% partially 2 6% no 0 0%

Was the workshop worth your time and effort? yes 34 94% partially 2 6% no 0 0%

Is it likely that you will work in the area of the workshop subject in the future? yes 22 61% partially 13 36% no 1 3%

Additional comments on your personal assessment I want to be more involved as a Sage developer in the future, thanks to this workshop. I am currently working on projects which are either similar to the ones on the workshop or were suggested during ...

Venue

Page 13 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

Your overall experience at MSRI 1 - Above satisfactory 28 78% 2 5 14% 3 2 6% 4 0 0% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The assistance provided by MSRI staff 1 - Above satisfactory 25 69% 2 7 19% 3 2 6% 4 1 3% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The overal atmosphere of MSRI 1 - Above satisfactory 32 89% 2 1 3% 3 0 0% 4 2 6% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

The physical surroundings

Page 14 of 15 Sage Days 22: Computing with Elliptic Curves, June 21, 2010 to July 2, 2010 at MSRI, Berkeley

1 - Above satisfactory 29 81% 2 5 14% 3 0 0% 4 1 3% 5 - Not satisfactory 1 3%

Above satisfactoryNot satisfactory

Additional comments on the venue Beautiful facilities! Beautiful place, excellent to study and think in. Thanks! Loud and uncontrollable air-conditioning; everything else was perfect, thank you!

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants. It was the best workshop I've ever been to. warn students ahead of time that the dorms do not have wireless internet access. Many students went out and bought ethernet cords, but it would have been e ...

Number of daily responses

Page 15 of 15

Summer School on Operator Algebras and Noncommutative Geometry June 14, 2010 to June 25, 2010 University of Victoria, Vancouver, Canada

Organizers: Heath Emerson, (University of Victoria) Thierry Giordano, (University of Ottawa) Marcelo Laca*, (University of Victoria) Ian Putnam, (University of Victoria) Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

Summer School on operator algebras and non-commutative geometry Victoria, June 14-26, 2010

Organizers: Heath Emerson, Mathematics and Statistics, University of Victoria Thierry Giordano, Mathematics and Statistics, University of Ottawa Marcelo Laca, Mathematics and Statistics, University of Victoria Ian Putnam, Mathematics and Statistics, University of Victoria.

Topics: Three lecture series (courses) on 1) The structure and classiﬁcation of nuclear C*-algebras, 2) KK-theory and the Baum-Connes conjecture, 3) C*-dynamical systems from number theory.

Methodology: Each lecture series consisted of ten one-hour lectures; in addition there were daily 1.5 hour discussion and problem solving sessions; detailed notes were made available through the PIMS website.

Scientific Program: Course title: The structure of nuclear C*-algebras. Lecturers: Nate Brown (Penn. State) and Andrew Toms (Purdue) Summary: This series of lectures introduced students to nuclear C*-algebras and current developments in their classification. They began with elementary facts and ended near the current frontier of research, on which there are very recent exciting developments due to W. Winter. Topics included K-theory, the Cuntz semigroup, decomposition rank, C*-dynamical systems and other things related to Elliott’s classification program. Course title: KK-theory and the Baum-Connes conjecture. Lecturers: Heath Emerson (Victoria) and R. Meyer (Göttingen) Summary: The Atiyah-Singer index theorem established an important link between topology and elliptic differential equations. One of the important ingredients was a homology theory for C*-algebras called K-theory. The Baum-Connes conjecture attempts to understand better how to calculate K-theory groups of particular C*-algebras. In the last 10 to 20 years it has sparked an extraordinary amount of activity and a lively interaction between C*- algebraists and specialists in other areas, like representation theory, geometric group theory, differential geometry, harmonic analysis and others. At the same time, K-theory is now used to classify C*-algebras. This workshop was an introduction to the techniques used to define and study the Baum-Connes conjecture, especially Kasparov’s equivariant KK-theory. In particular, we started with a rapid introduction to K-theory for C*-algebras, which comple- mented the minicourse of Brown and Toms on classification of C*- algebras. The emphasis

Page 2 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

throughout was on Kasparov’s approach to the Baum-Connes conjecture, using duality, and on Baum and Connes’ perspective on the index theorem, using geometric cycles to describe K-homology. Course title: C*-dynamical systems from number theory. Lecturers: Marcelo Laca (Victoria) and Sergey Neshveyev (Oslo) Summary: This lecture series started with the necessary background on algebraic number theory and on dynamical systems and their equilibrium states. We then reviewed key examples, some exhibiting uniqueness of equilibrium and some exhibiting non-uniqueness (i.e. phase transitions). Following this we presented and analyzed in detail the remarkable system, due to Bost and Connes, exhibiting a phase transition with the spontaneous breaking, at low temperature, of a symmetry given by the Galois group of the maximal abelian extension of the rationals. The second half of the minicourse was aimed to reach the state of the art in the subject and to shed light on its connection with explicit class ﬁeld theory. It included the phase transition of the generalization of the Bost-Connes system to imaginary quadratic ﬁelds due to Connes, Marcolli and Ramachandran and that of the GL2-system of Connes and Marcolli. We developed some of the background, basic constructions and examples as guided exercises suitable for informal discussion during the afternoon sessions.

Accomplishments and assessment of impact: The lectures and the discussion sessions were very well attended for the duration of the summer school. This level of participation and the level of the questions and solutions to the suggested problems indicated to us a high degree of engagement. There was ample opportunity for students to meet each other and the lecturers, which had the eﬀect of promoting the areas of research covered as being ‘friendly’. The host institution beneﬁted from the international exposure and we hope to see this represented in more high quality graduate students applying to do their studies here. We were left with the impression that the event was very well received, that the participants did learn from the lectures, and that the 10 lecture format worked quite well. At the end we were very happy to hear several participants asking about when the next summer school was going to take place.

Scientific highlights of the event: (some comments excerpted from the formal survey carried out by PIMS) The talks by Brown and Toms. The discussions with the professors who are working on my field. The clear presentations from all the speakers. Meeting some other PhD students from different countries and different background was pretty interesting too. The new picture of classification theory. I really liked the final lecture of the classification series, since it put a lot of the current classification work into perspective and talked about the future of the subject in a very inspiring and accessible way. The courses were really well given and the subjects motivated. It was definitely an event worth attending. It is one of the best summer schools that I have been to.

Page 3 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

Participants

Summer School on operator algebras and non-commutative geometry Victoria, June 14-26, 2010

Adema Josh UVic Boey Ted Univ. of Waterloo Brothier Arnaud Berkeley Bravo Blanca CINVESTAV (IPN) Mexico City Carderi Alessandro University of Rome Carrin Jos R. Purdue University Chebotarov Dmytro University of Southern California Crisp Tyrone Penn State Deeley Robin UVic Francis Michael UVic Georgescu Magda UVic Gillaspy Elizabeth Dartmouth College Hines Taylor Arizona State Univ. Hong Seunghun Penn State Hosseini Abbas Universiti Sains Malaysia Hynes Siri-Maln NTNU, Trondheim Isely Olivier Universit de Neuchatel Julien Antoine Universit Lyon Killough Brady Mount Royal Univ., Calgary Kornell Andre UC Berkeley Lee Hyun Ho SNU, Korea Lee Jaehyup SNU, Korea Leung Ho Hon Cornell University Li Xin Univ. Muenster Mahanta Snigdhayan Johns Hopkins Univ. Mahoney Matthew Dartmouth College McCann Shawn Univ. of Calgary Norling Magnus Dahler Norwegian Univ Palm Marc Univ. G¨ottingen Palma Rui Univ of Oslo Papish Vlad Wairever Inc. / Calgary Quingyun Wang Washington State Robson Lance UVic Sangha Amandip Univ. Oslo Shahada Mayada United Arab Emirates University

Page 4 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

Schedler Travis MIT (CLE Moore Instructor) Sierakowski Adam Fields Institute/Toronto Song Lei University of Illinois, Chicago Song Yanli Penn State Univ. Starling Charles Uvic (previously at U of Ottawa) Tian-Yu Tan Penn State Univ. Tseng Michael Penn State Univ. Otgonbayar Uuye Univ. of Copenhagen vanFrankenhuijsen Machiel Utah Valley University Wanvik Martin NTNU, Trondheim in Norway Whittaker Mike UVic Willett Rufus Vanderbilt Univ., Nashville Yashinski Allan Penn State

Page 5 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June14,2010to25,attheUniversityofVictoria,Vancouver,Canada and Noncommutative Summer SchoolonOperatorAlgebras

PProgram NCG Summer School 2010 - Week # 1 , June 14th - June 18th SSM BUILDING

Monday,Monday, June 14 Tuesday,Tuesday, June 15 Wednesday,Wednesday, June 16 Thursday,Thursday, June 17 Friday,Friday, June 18 SSM, R Roomoom A104 SSM, R Roomoom A104 SSM, R Roomoom A104 SSM, R Roomoom A104 SSM, R Roomoom A104

8:30 am - 9:10 am RegistrationRegistration //W Welcome l

9109:10 am - 10:10 1010 am TheTh structure t t of f nuclear l C C*C*-al algebras, lgebras b , Andrew Toms

10:10 am - 10:30 am Coffee Break (Lobby of SSM) Page 6of 17

10:3010:30 am - 11 11:30:30 am KK-theoryKK-theory and the Baum Baum-Connes-Connes conjecture HthEHeath Emerson and dRlfM Ralf MeyerMeyer

RegistrationReggistration C Continuedontinued 11:30 am - 2:00 pm Lunch Lunch

2:00 pm - 3:00 pm CC**-dynamical-dynamical systems from number theory Marcelo LacaLaca

3:00 pm - 3:30 pm Coffee Break (Lobby of SSM)

3:30 pm - 5:00 pm Informal discussion / Problems Summer School on Operator Algebras and Noncommutative Geometry, June14,2010to25,attheUniversityofVictoria,Vancouver,Canada and Noncommutative Summer SchoolonOperatorAlgebras

PProgram NCG Summer School 2010 - Week # 2, June 21 - 25 SSM BUILDING

Monday,Monday, June 21 Tuesday,Tuesday, June 22 Wednesday,Wednesday, June 23 Thursday,Thursday, June 24 Friday,Friday, June 25 SSM, R Roomoom A104 SSM, R Roomoom A104 SSM, R Roomoom A104 SSM, R Roomoom A120 SSM, R Roomoom A120

9:10 am - 10:10 am The structure of nuclear C*- -algebrasalgebras,, NateNate B Brownrown

10:10 am - 10:30 am Coffee Break (Lobby of SSM)

1010:30 30 am - 1111:30 30 am KK- theorytheoryyj andand thethe BaumBaum- ConnesConnes conjectureconjecture Ralf Meyer and Heath Emerson Page 7of 17

11:3011:30 am - 2 2:00:00 pm p LunchLunch

2:002:00 pm pp - 3 3:00:00 pm C*- dynamicaldynamyyical sys systemstems fromfrom numbernumber theorytheoryy Sergey Neshveyev

3:00 pm - 3:30 pm Coffee Break (Lobby of SSM)

3:30 pm - 5:00 pm Informal discussion / Problems Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

Invited Participants

firstname lastname institutionname Blanca Bravo National Polytechnic Institute Jose Carrion Purdue University Dmytro Chebotarov University of Southern California Tyson Crisp Pennsylvania State University Elizabeth Gillaspy Dartmouth College Andre Kornell University of California Lei Song University of Illinois Michael Tseng Pennsylvania State University Qingyun Wang Inner Mongolia Finance and Economics College

Page 8 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

Invited Participants

Participants 9

Gender 9 Male 66.67% 6 Female 22.22% 2 Declined to state 11.11% 1

Ethnicity* 9 White 33.33% 3 Asian 33.33% 3 Hispanic 22.22% 2 Pacific Islander 0.00% 0 Black 0.00% 0 Native American 0.00% 0 Declined to state 11.11% 1 * ethnicity specifications are not exclusive

Page 9 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

responses

See complete responses

Topic presentation and organization

Did the various topics within the workshop integrate into a coherent picture? yes 2 50% partially 2 50% no 0 0% no opinion 0 0%

Were the speakers generally clear and well organized in their presentation? above satisfactory 1 25% satisfactory 3 75% not satisfactory 0 0% no opinion 0 0%

Was there too much material presented; was the workshop too ambitious?

Page 11 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada too much 0 0% just right 3 75% not enough 1 25% no opinion 0 0%

Was the problem session helpful? yes 1 25% partially 2 50% no 1 25% no opinion 0 0%

Additional comments on the topic presentation and organization Some of the speakers were excellent; others were hard to follow Excellent presentation and organization

Personal assessment

Was your background adequate to access a reasonable portion of the material? yes 3 75% partially 1 25% no 0 0%

Page 12 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada Did the workshop increase your interest in the subject? yes 3 75% partially 1 25% no 0 0%

Was the workshop worth your time and effort? yes 4 100% partially 0 0% no 0 0%

Is it likely that you will work in the area of the workshop subject in the future? yes 2 50% partially 2 50% no 0 0%

How would you evaluate your interaction with other participants?

Page 13 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada 1 - above satisfactory 2 50% 2 2 50% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Page 14 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada

Additional comments on your personal assessment Some of the topics became more interesting; some less. My research will focus on areas of noncommutative geometry that weren't covered in the lectures at the workshop.

Venue

Please rate the different categories

Your overall experience 1 - above satisfactory 3 75% 2 1 25% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The assistance provided by staff 1 - above satisfactory 3 75% 2 1 25% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The physical surroundings

Page 15 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada 1 - above satisfactory 3 75% 2 1 25% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on the venue

Accommodation and Food

Please rate the different categories

The summer school accommodation 1 - above satisfactory 2 50% 2 2 50% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

The food provided

Page 16 of 17 Summer School on Operator Algebras and Noncommutative Geometry, June 14, 2010 to June 25, 2010 at the University of Victoria, Vancouver, Canada 1 - above satisfactory 2 50% 2 2 50% 3 0 0% 4 0 0% 5 - not satisfactory 0 0%

above satisfactorynot satisfactory

Additional comments on accommodation and food

Thank you for completing this survey

We welcome any additonal comments or suggestions you may have to improve the overall experience for future participants.

Number of daily responses

Page 17 of 17