DOCSLIB.ORG

Mathematical Sciences Research Institute Annual Report, 2016-2017

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Annual Report on the Mathematical Sciences Research Institute 2016–2017 activities supported by NSF Grant DMS-1440140 June 1, 2016 to May 31, 2017 July 2017 Mathematical Sciences Research Institute Annual Report, 2016-2017 1. Overview of Activities ................................................................................................................... 1 1.1 New Developments ............................................................................................................ 1 1.2 Summary of Demographic Data for 2016-17 Activities .................................................... 7 1.3 Scientific Programs and their Associated Workshops ....................................................... 9 1.4 Scientific Activities Directed at Underrepresented Groups in Mathematics ................... 11 a. Connections for Women Workshops .................................................................. 11 b. MSRI-UP 2016 (DMS-1156499) ........................................................................ 12 c. Modern Math Workshop at SACNAS ................................................................ 12 d. Blackwell-Tapia Conference 2016 ..................................................................... 12 1.5 Summer Graduate Schools 2016 ...................................................................................... 12 1.6 Other Scientific Workshops ............................................................................................. 13 1.7 Education & Outreach Activities ..................................................................................... 14 a. Critical Issues in Mathematics Education 2017: Observing for Access, Power, and Participation in Mathemtics Classrooms as a Strategy to Improve Mathematics Teaching and Learning (NSF Grants DLR-1461358 and DLR- 1738702) ............................................................................................................. 14 b. National Math Festival 2017 (NSF Supplement Grant DMS-1733966) ............. 14 1.8 Program Consultants List in 2016-17 .............................................................................. 15 2. Program and Workshop Data .................................................................................................... 16 2.1 Program Members List .................................................................................................... 16 2.2 Program Members Summary ........................................................................................... 16 2.3 Program Members Demographic Data ............................................................................ 17 2.4 Workshop Participant List ............................................................................................... 19 2.5 Workshop Participant Summary ...................................................................................... 19 2.6 Workshop Participant Demographic Data ....................................................................... 20 2.7 Program Publication List ................................................................................................. 22 2.8 Program Publication Work-in-Progress List .................................................................... 22 3. Postdoctoral Program ................................................................................................................. 23 3.1 Description of Activities .................................................................................................. 23 3.2 Postdoctoral Fellow Placement List ................................................................................. 72 3.3 Postdoctoral Fellow Participant Summary ....................................................................... 67 3.4 Postdoctoral Fellow Demographic Data .......................................................................... 68 3.5 Postdoctoral Research Member Placement List ............................................................... 70 3.6 Postdoctoral Research Member Summary ....................................................................... 70 4. Graduate Program ...................................................................................................................... 70 4.1. Summer Graduate Schools (2016) ................................................................................... 70 4.2. Summer Graduate School Data ........................................................................................ 72 4.3. Program Associates .......................................................................................................... 76 4.4. Program Associate Data ................................................................................................... 76 4.5. Graduate Student List ...................................................................................................... 79 4.6. Graduate Student Data ..................................................................................................... 79 5. Undergraduate Program in 2016 (MSRI-UP) .......................................................................... 80 5.1. Description of Undergraduate Program ........................................................................... 80 11. Appendix – Final Reports of Activities in 2016–17 .................................................................. 82 PROGRAM REPORTS i. No. 278: Geometric Group Theory ..................................................................................... 83 ii. No. 297: Analytic Number Theory ................................................................................... 102 iii. No. 300: Harmonic Analysis ............................................................................................. 126 iv. No. 320: Complementary Program (2016-17) .................................................................. 146 WORKSHOP REPORTS v. No. 768: Connections for Women: Geometric Group Theory .......................................... 159 vi. No. 769: Introductory Workshop: Geometric Group Theory ............................................ 190 vii. No. 770: Amenability, coarse embeddability and fixed point properties .......................... 219 viii. No. 771: Geometry of mapping class groups and Out(Fn) ............................................... 248 ix. No. 772: Groups acting on CAT(0) spaces ....................................................................... 278 x. No. 800: Connections for Women: Analytic Number Theory .......................................... 309 xi. No. 801: Introductory Workshop: Analytic Number Theory ............................................ 340 xii. No. 802: Connections for Women: Harmonic Analysis.................................................... 369 xiii. No. 803: Introductory Workshop: Harmonic Analysis ..................................................... 401 xiv. No. 805: Recent Developments in Harmonic Analysis ..................................................... 431 xv. No. 810: Recent Developments in Analytic Number Theory ........................................... 461 xvi. No. 826: Hot Topics: Galois Theory of Periods and Applications ................................... 491 xvii. NATIONAL MATH FESTIVAL 2017............................................................................. 519 SUMMER GRADUATE SCHOOLS xviii. No. 767: An Introduction to Character Theory and the McKay Conjecture ..................... 532 xix. No. 773: Mixed Integer Nonlinear Programming: Theory, algorithms and applications . 551 xx. No. 775: Seminaire de Mathematiques Superieures 2016: Dynamics of Biological Systems ..... 570 xxi. No. 776: Harmonic Analysis & Elliptic Equations on real Euclidean Spaces & on Rough Sets .. 595 xxii. No. 777: Chip Firing and Tropical Curves ........................................................................ 615 xxiii. No. 778: Electronic Structure Theory ............................................................................... 634 1. Overview of Activities This annual report covers MSRI’s projects and activities supported by the NSF core grant, DMS- 1440140, during the period of June 1st, 2016 to May 31st, 2017. 1.1 New Developments The year 2016–17 was an exciting one. In fall 2016, we held a jumbo program: Geometric Group Theory, with lead organizer Mark Feighn (Rutgers). In Spring 2017, we held two programs: Analytic Number Theory, led by Terence Tao (UCLA), and Harmonic Analysis, led by Michael Christ (Berkeley) and Michael Lacey (Georgia Tech). All three programs were very popular, and their workshops well attended. All programs had stellar researchers with four of them awarded funding by the Clay Mathematics Institute: Manjul Bhargava, Rodney Heath- Brown, Karen Vogtmann, and Alexander Volberg. Manjul Bhargava and Terry Tao need no introduction, as their pioneering work in several areas of number theory and harmonic analysis yielded breakthroughs that didn’t seem possible ten years ago. Their Fields Medals (2014, 2016), Infosys, Fermat, Cole, Salem, Polya, and Breakthrough prizes (and many other awards) simply confirm what everyone knows: they are exceptional researchers producing extraordinary mathematics. Prof. Tao mentored a postdoc, Ayla Gafni, whose experience at MSRI was exceptionally productive. As she mentions in her end of semester report (see section 3), prior to her PD fellowship at MSRI she did not have many collaborators. She now lists 11 collaborators and six projects started here which are in various stages of completion.
Recommended publications
  • Curriculum Vitae Education Professional Positions Honors And

    Curriculum Vitae Education Professional Positions Honors And

    Curriculum Vitae Xiuxiong Chen Education • PhD., Pure Mathematics, University of Pennsylvania, 1994. • M.A., Graduate School of Academic Sinica, Beijing, China, 1989. • B.A., Pure Mathematics, University of Science and Technology of China, Hefei, China, 1987. Professional positions • 09/2010–, Professor, Stony Brook University. • 01/2007–06/2007, Visiting Professor, Princeton University. • 2005–2010, Professor, University of Wisconsin at Madison. • 2002-2005, Associate Professor, University of Wisconsin at Madison. • 1998-2002, Assistant Professor, Princeton University. • 1996-1998, NSF Post-doctoral Fellow, Stanford University. • 1994-1996, Instructor, McMaster University, Canada. Honors and Awards • 1996-2000, National Science foundation postdoctoral Fellowship. • 08/2002, Invited address at International Congress of Mathematicians, Beijing, China. • 04/2005, Invited address at AMS regional meeting in Newark, Delware. • 04/09/2010-04/11/2010, Invited lecture at 25th Geometry Festival, Courant Institute. • 2015, Fellow of the American Mathematical Society. • 2016, Simons Fellow in Mathematics. • 2019, Veblen Prize in Geometry. • 2019, Simons Investigator Award. Xiuxiong Chen Curriculum vitae PhD. Students and Theses Supervised/co-supervised • Yingyi Wu (PhD., 2005, University of Science and Technology). Some problems on HCMU metrics in Riemannian Surfaces. • Brian Weber (PhD., 2007, UW-Madison), Moduli Spaces of Extremal Kahler¨ Manifolds. • Weiyong He (PhD., 2007, UW-Madison), Extremal Metrics, The Stability Conjecture and the Cal- abi Flow. • Haozhao Li (PhD, 2007, Peking University), Energy Functionals and Kahler-Ricci¨ Flow. • Bing Wang (PhD., 2008, UW-Madison), On the Extension of the Ricci flow. • Yudong Tang (PhD., 2008, UW-Madison), Geodesic Rays and Test Configurations. • Weidong Yin(PhD., 2009, UW-Madison), Weak Solution of Yang-Mills Flow in Dimension N?4: • Song Sun (PhD., 2010, UW-Madison), Kempf-Ness theorem and uniqueness of extremal metrics.
  • Curriculum Vitae

    Curriculum Vitae

    Curriculum Vitae Larry Guth Education B.S. Mathematics, Yale University, 2000 PhD Mathematics, MIT, 2005 Employment Samelson Fellow, Stanford University 2005-6 Szego Assistant Professor, Stanford University, 2006 - 2008 National Science Foundation Postdoctoral Fellow, 2006 - 2008 Tenure-stream Assistant Professor, University of Toronto, 2008 - 2011 Member, Institute for Advanced Study, 2010 - 2011 Professor, New York University, 2011 - 2012 Professor, MIT, 2012 - Fellowships National Science Foundation Graduate Fellowship, 2001 - 2003 National Science Foundation Postdoctoral Fellowship , 2006 - 2008 Alfred P. Sloan Research Fellowship, 2010 - 2014 Simons Investigator, 2014 - Honors Salem prize 2013 Invited talks Invited sectional speaker at the 2010 International Congress of Mathematics Marston Morse lectures, IAS, 2013 Namboodiri lectures, University of Chicago, 2015 1 Selected publications 1. Lipshitz maps from surfaces, Geom. Funct. Anal. 15 (2005), no. 5, 1052-109 2. The width-volume inequality, Geom. Funct. Anal. 17 (2007) no. 4, 1139-1179 3. Notes on Gromov's systolic estimate, Geom. Dedicata 123 (2006) 113-129 4. Symplectic embeddings of polydisks, Invent. Math. 172 (2008) no. 3, 477-489 5. Minimax problems related to cup powers and Steenrod squares, Geom. Funct. Anal. 18 (2009), no. 6, 1917{1987 6. The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263-286. 7. Systolic inequalities and minimal hypersurfaces, Geom. Funct. Anal. 19 (2010), no. 6, 1688-1692. 8. Volumes of balls in large Riemannian manifolds, Ann. of Math. (2) 173 (2011), no. 1, 5176. 9. Area-expanding embeddings of rectangles, preprint 10. Algebraic methods in discrete analogs of the Kakeya problem (joint with Nets Katz), Adv.
  • Curriculum Vitae Fernando Codá Marques January 16Th, 2019

    Curriculum Vitae Fernando Codá Marques January 16Th, 2019

    Curriculum Vitae Fernando Cod´aMarques January 16th, 2019 Personal information Name: Fernando Cod´aMarques Date of birth: October 8th of 1979 Nationality: Brazilian Address Princeton University Fine Hall, Washington Road Princeton NJ 08544-1000 USA Phone: (609) 258-1769 Fax: (609) 258-1367 Education 2000-2003 Ph.D. in Mathematics Cornell University, C. U., Ithaca/NY USA Thesis Advisor : Jos´eF. Escobar Title : Existence and compactness theorems on conformal deformations of metrics Scholarship from : Conselho Nacional de Desenvolvimento Cient´ıficoe Tecnol´ogico(CNPq) 1998-1999 Mathematics M.S. IMPA, Rio de Janeiro/RJ Brazil Scholarship from : Conselho Nacional de Desenvolvimento Cient´ıficoe Tecnol´ogico(CNPq) 1996-1999 Mathematics B.S. UFAL - Universidade Federal de Alagoas Macei´o,Alagoas - Brazil Employment history 2003-2007 Assistant Professor, IMPA 2007-2010 Associate Professor, IMPA 2010-2014 Professor, IMPA 2014- Professor, Princeton University Visiting Positions 2018 Distinguished Visitor Professor, IAS, Princeton - Special Program 2018-2019: \Variational Methods in Geometry" 2017 Dean's Distinguished Visiting Professor, Fields Institute, Toronto, Canada 2013-2014 Ecole´ Polytechnique, Ecole´ Normale Sup´erieureand Universit´eParis-Est Marne la Vall´ee,Paris, France 2012 Institut Henri Poincar´e,Paris, France (1 month) 2011 Stanford University, USA (2 months) 2011 Institut Fourier, Grenoble, France (1 month) 2010 Stanford University, USA (3 months) 2009 Stanford University, USA (1 month) 2008 Member of the Institute for Advanced
  • CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA

    CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA

    A MERICAN M ATHEMATICAL S OCIETY CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA 1:00 PM Carina Curto, Pennsylvania State University What can topology tell us about the neural code? Surprising new applications of what used to be thought of as “pure” mathematics. 2:00 PM Yuval Peres, Microsoft Research and University of California, Berkeley, and Lionel Levine, Cornell University Laplacian growth, sandpiles and scaling limits Striking large-scale structure arising from simple cellular automata. 3:00 PM Timothy Gowers, Cambridge University Probabilistic combinatorics and the recent work of Peter Keevash The major existence conjecture for combinatorial designs has been proven! 4:00 PM Amie Wilkinson, University of Chicago What are Lyapunov exponents, and why are they interesting? A basic tool in understanding the predictability of physical systems, explained. Organized by David Eisenbud, Mathematical Sciences Research Institute Introduction to the Current Events Bulletin Will the Riemann Hypothesis be proved this week? What is the Geometric Langlands Conjecture about? How could you best exploit a stream of data flowing by too fast to capture? I think we mathematicians are provoked to ask such questions by our sense that underneath the vastness of mathematics is a fundamental unity allowing us to look into many different corners -- though we couldn't possibly work in all of them. I love the idea of having an expert explain such things to me in a brief, accessible way. And I, like most of us, love common-room gossip.
  • Iakovos Androulidakis Curriculum Vitæ, October 2020

    Iakovos Androulidakis Curriculum Vitæ, October 2020

    Iakovos Androulidakis Curriculum Vitæ, October 2020 Personal data Nationality Greek. Citizenship Greek. Home 19, Leonida Drosi Street, 11474, Athens, Greece. address Date of birth February 6, 1973. Place of Athens, Greece. birth PhD University of Sheffield, U.K., January 17, 2002. Positions Nov 2016 – Associate Professor (tenured), National and Kapodistrian University of Athens today (NKUA). Jan. 2012 – Assistant Professor (tenure track), National and Kapodistrian University of Athens Oct 2016 (NKUA). Aug. 2009 – Postdoctoral Researcher (DFG), Institute of Mathematics, University of Göttingen. July 2011 Sept. 2008 – Postdoctoral Researcher (FCT), University of Porto. June 2009 Oct 2006 – Visiting Assistant Professor (P.D. 407), Department of Mathematics, University of June 2008 Crete. Sept. 2005 – Research Assistant to Prof. A. Cattaneo, Institute of Mathematics, University of Sept. 2006 Zürich. Sept. 2004 – Postodoctoral Researcher (EU-RTN ”Quantum Spaces and Noncommutative July 2005 Geometry”), Departement de Mathématiques, Paris 7 Denis Diderot. May 2002 – National service and medical recovery. Aug. 2004 Sept. 2001 – Postdoctoral Researcher (EU-RTN ”Differential Geometry Endeavour”), Feb. 2002 Instituto Superior Tecnico, Lisbon. Sept. 10, PhD viva voce, University of Sheffield. 2001 Panepistimiopolis – 15784 Athens +30 210 7276423 • +30 210 7276378 • [email protected] http://scholar.uoa.gr/iandroul/ Grants/Awards/Prizes 2015 “Chercheur Visiteur” at Paris 7 Denis Diderot (3900 euros). DFG funding for short visits to University of Göttingen (4800 euros). “Shapiro Visiting Professorship”, Penn State (2500 euros). 2013 “Konstantine Karatheodory” prize (NKUA) 2012 Prize of the Academy of Athens to common publication with V. Nestoridis (prize awarded to V. Nestoridis) 2011 Marie Curie Career Integration Grant (50000 euros). http://users.uoa.gr/ ~iandroul/NCGSF.html 2011 “Maitre de Conferences Visiteur”, Université Toulouse Paul Sabatier.
  • For Your Information

    For Your Information

    fyi.qxp 3/18/98 3:19 PM Page 244 For Your Information structure federal support. The study is part of a larger ef- International Study of fort at the Academy to gauge where the U.S. stands in- Mathematics and Science ternationally in scientific research. The motivation comes from a 1993 report by the Committee on Science, Engi- Achievement neering, and Public Policy (COSEPUP), which set forth strate- gies for making decisions about how best to use federal The first installment of results from the Third International research funds. COSEPUP is a committee of the NAS, the Mathematics and Science Study (TIMSS) was released on No- National Academy of Engineering, and the Institute of Med- vember 20. This first batch of data pertains to achievement icine. The COSEPUP report recommended that the U.S. aim of eighth-graders; later releases will focus on fourth- and to be the world leader in certain critical fields and to be twelfth-graders. The study found that U.S. eighth-graders among the leaders in other areas. The report urged field- performed below the international average in mathemat- by-field assessments by independent panels of researchers ics but slightly above average in science. The U.S. was in the field, researchers in closely related fields, and users among thirty-three countries in which there was no sta- of the research. The mathematical sciences study is the first tistically significant difference between the performance such assessment. If this project is successful, the Academy of eighth-grade boys and girls in mathematics. The study will follow suit with other areas.
  • What Are Lyapunov Exponents, and Why Are They Interesting?

    What Are Lyapunov Exponents, and Why Are They Interesting?

    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 54, Number 1, January 2017, Pages 79–105 http://dx.doi.org/10.1090/bull/1552 Article electronically published on September 6, 2016 WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING? AMIE WILKINSON Introduction At the 2014 International Congress of Mathematicians in Seoul, South Korea, Franco-Brazilian mathematician Artur Avila was awarded the Fields Medal for “his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.”1 Although it is not explicitly mentioned in this citation, there is a second unify- ing concept in Avila’s work that is closely tied with renormalization: Lyapunov (or characteristic) exponents. Lyapunov exponents play a key role in three areas of Avila’s research: smooth ergodic theory, billiards and translation surfaces, and the spectral theory of 1-dimensional Schr¨odinger operators. Here we take the op- portunity to explore these areas and reveal some underlying themes connecting exponents, chaotic dynamics and renormalization. But first, what are Lyapunov exponents? Let’s begin by viewing them in one of their natural habitats: the iterated barycentric subdivision of a triangle. When the midpoint of each side of a triangle is connected to its opposite vertex by a line segment, the three resulting segments meet in a point in the interior of the triangle. The barycentric subdivision of a triangle is the collection of 6 smaller triangles determined by these segments and the edges of the original triangle: Figure 1. Barycentric subdivision. Received by the editors August 2, 2016.
  • The Book of Abstracts

    The Book of Abstracts

    1st Joint Meeting of the American Mathematical Society and the New Zealand Mathematical Society Victoria University of Wellington Wellington, New Zealand December 12{15, 2007 American Mathematical Society New Zealand Mathematical Society Contents Timetables viii Plenary Addresses . viii Special Sessions ............................. ix Computability Theory . ix Dynamical Systems and Ergodic Theory . x Dynamics and Control of Systems: Theory and Applications to Biomedicine . xi Geometric Numerical Integration . xiii Group Theory, Actions, and Computation . xiv History and Philosophy of Mathematics . xv Hopf Algebras and Quantum Groups . xvi Infinite Dimensional Groups and Their Actions . xvii Integrability of Continuous and Discrete Evolution Systems . xvii Matroids, Graphs, and Complexity . xviii New Trends in Spectral Analysis and PDE . xix Quantum Topology . xx Special Functions and Orthogonal Polynomials . xx University Mathematics Education . xxii Water-Wave Scattering, Focusing on Wave-Ice Interactions . xxiii General Contributions . xxiv Plenary Addresses 1 Marston Conder . 1 Rod Downey . 1 Michael Freedman . 1 Bruce Kleiner . 2 Gaven Martin . 2 Assaf Naor . 3 Theodore A Slaman . 3 Matt Visser . 4 Computability Theory 5 George Barmpalias . 5 Paul Brodhead . 5 Cristian S Calude . 5 Douglas Cenzer . 6 Chi Tat Chong . 6 Barbara F Csima . 6 QiFeng ................................... 6 Johanna Franklin . 7 Noam Greenberg . 7 Denis R Hirschfeldt . 7 Carl G Jockusch Jr . 8 Bakhadyr Khoussainov . 8 Bj¨ornKjos-Hanssen . 8 Antonio Montalban . 9 Ng, Keng Meng . 9 Andre Nies . 9 i Jan Reimann . 10 Ludwig Staiger . 10 Frank Stephan . 10 Hugh Woodin . 11 Guohua Wu . 11 Dynamical Systems and Ergodic Theory 12 Boris Baeumer . 12 Mathias Beiglb¨ock . 12 Arno Berger . 12 Keith Burns . 13 Dmitry Dolgopyat . 13 Anthony Dooley .
  • 1914 Martin Gardner

    1914 Martin Gardner

    ΠME Journal, Vol. 13, No. 10, pp 577–609, 2014. 577 THE PI MU EPSILON 100TH ANNIVERSARY PROBLEMS: PART II STEVEN J. MILLER∗, JAMES M. ANDREWS†, AND AVERY T. CARR‡ As 2014 marks the 100th anniversary of Pi Mu Epsilon, we thought it would be fun to celebrate with 100 problems related to important mathematics milestones of the past century. The problems and notes below are meant to provide a brief tour through some of the most exciting and influential moments in recent mathematics. No list can be complete, and of course there are far too many items to celebrate. This list must painfully miss many people’s favorites. As the goal is to introduce students to some of the history of mathematics, ac- cessibility counted far more than importance in breaking ties, and thus the list below is populated with many problems that are more recreational. Many others are well known and extensively studied in the literature; however, as our goal is to introduce people to what can be done in and with mathematics, we’ve decided to include many of these as exercises since attacking them is a great way to learn. We have tried to include some background text before each problem framing it, and references for further reading. This has led to a very long document, so for space issues we split it into four parts (based on the congruence of the year modulo 4). That said: Enjoy! 1914 Martin Gardner Few twentieth-century mathematical authors have written on such diverse sub- jects as Martin Gardner (1914–2010), whose books, numbering over seventy, cover not only numerous fields of mathematics but also literature, philosophy, pseudoscience, religion, and magic.
  • President's Report

    President's Report

    Newsletter VOLUME 43, NO. 6 • NOVEMBER–DECEMBER 2013 PRESIDENT’S REPORT As usual, summer flew by all too quickly. Fall term is now in full swing, and AWM is buzzing with activity. Advisory Board. The big news this fall is the initiation of an AWM Advisory Board. The Advisory Board, first envisioned under Georgia Benkart’s presidency, con- The purpose of the Association for Women in Mathematics is sists of a diverse group of individuals in mathematics and related disciplines with distinguished careers in academia, industry, or government. Through their insights, • to encourage women and girls to breadth of experience, and connections with broad segments of the mathematical study and to have active careers in the mathematical sciences, and community, the Board will seek to increase the effectiveness of AWM, help with fund- • to promote equal opportunity and raising, and contribute to a forward-looking vision for the organization. the equal treatment of women and Members of the Board were selected to represent a broad spectrum of academia girls in the mathematical sciences. and industry. Some have a long history with AWM, and others are new to the orga- nization; all are committed to forwarding our goals. We are pleased to welcome the following Board members: Mary Gray, Chair (American University) Jennifer Chayes (Microsoft Research) Nancy Koppel (Boston University) Irwin Kra (Stony Brook University) Joan Leitzel (University of New Hampshire, Ohio State University) Jill Mesirov (Broad Institute) Linda Ness (Applied Communication Sciences) Richard Schaar (Texas Instruments) IN THIS ISSUE Mary Spilker (Pfizer) Jessica Staddon (Google) 4 AWM Election 14 Benkart Named In addition, the President, Past President (or President Elect) and Executive Noether Lecturer Director of AWM are also members of the Board.
  • Ergodic Currents Dual to a Real Tree Thierry Coulbois, Arnaud Hilion

    Ergodic Currents Dual to a Real Tree Thierry Coulbois, Arnaud Hilion

    Ergodic currents dual to a real tree Thierry Coulbois, Arnaud Hilion To cite this version: Thierry Coulbois, Arnaud Hilion. Ergodic currents dual to a real tree. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2016, 36 (3), pp.745-766. 10.1017/etds.2014.78. hal- 01481866 HAL Id: hal-01481866 https://hal.archives-ouvertes.fr/hal-01481866 Submitted on 3 Mar 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ERGODIC CURRENTS DUAL TO A REAL TREE THIERRY COULBOIS, ARNAUD HILION Abstract. Let T be an R-tree with dense orbits in the boundary of Outer space. When the free group FN acts freely on T , we prove that the number of projective classes of ergodic currents dual to T is bounded above by 3N − 5. We combine Rips induction and splitting induction to define unfolding induction for such an R-tree T . Given a current µ dual to T , the unfolding induction produces a sequence of approximations converging towards µ. We also give a unique ergodicity criterion. 1. Introduction 1.1. Main results. Let FN be the free group with N generators.
  • Notes on Sela's Work: Limit Groups And

    Notes on Sela's Work: Limit Groups And

    Notes on Sela's work: Limit groups and Makanin-Razborov diagrams Mladen Bestvina∗ Mark Feighn∗ October 31, 2003 Abstract This is the first in a series of papers giving an alternate approach to Zlil Sela's work on the Tarski problems. The present paper is an exposition of work of Kharlampovich-Myasnikov and Sela giving a parametrization of Hom(G; F) where G is a finitely generated group and F is a non-abelian free group. Contents 1 The Main Theorem 2 2 The Main Proposition 9 3 Review: Measured laminations and R-trees 10 4 Proof of the Main Proposition 18 5 Review: JSJ-theory 19 6 Limit groups are CLG's 22 7 A more geometric approach 23 ∗The authors gratefully acknowledge support of the National Science Foundation. Pre- liminary Version. 1 1 The Main Theorem This is the first of a series of papers giving an alternative approach to Zlil Sela's work on the Tarski problems [31, 30, 32, 24, 25, 26, 27, 28]. The present paper is an exposition of the following result of Kharlampovich-Myasnikov [9, 10] and Sela [30]: Theorem. Let G be a finitely generated non-free group. There is a finite collection fqi : G ! Γig of proper quotients of G such that, for any homo- morphism f from G to a free group F , there is α 2 Aut(G) such that fα factors through some qi. A more precise statement is given in the Main Theorem. Our approach, though similar to Sela's, differs in several aspects: notably a different measure of complexity and a more geometric proof which avoids the use of the full Rips theory for finitely generated groups acting on R-trees, see Section 7.