MATHDepartment of Mathematics CornellMATTERS University Ithaca NY November 2010 Letter From The Chair, Laurent Saloff-Coste I want to thank the staff and The next decade will role in allowing specific Cornell faculty of the department for their undoubtedly be dominated by hiring programs to be worldwide leaders in work and support during what, not activities in a very competitive their field. Obviously, this ambitious surprisingly, turned out to be a very environment. It is likely that half goal calls for a premier College of difficult year. Dan Barbasch had the department will change during Arts and Sciences, including a first- managed the first round of budget the next ten years or so. The result rate department of mathematics. As cuts efficiently, leaving our program of these hiring activities will have a a direct consequence of the budget in good shape. The significance of tremendous effect on the future of crisis, I had no choice but to collect the second round of cuts, similar in mathematics at Cornell. and immerse myself in a great size to the first round, will only be Cornell belongs to a relatively quantity of data searching to answer understood over time. small and very select group of the question: what are the important Throughout this challenging institutions that aspire to exceptional characteristics of a premier year, the department maintained quality and leadership over the department of mathematics? a high level of very successful entire spectrum of intellectual Data regarding the 100 activities in the areas of instruction, activities. This bold, institution- departments of mathematics in research and outreach including wide aspiration plays an essential Continued on page 3. the Chelluri, Kieval, and Evans Lectures, and the annual Topology Math Awareness Month Festival. Let me acknowledge the by Mary Ann Huntley very positive impact of the generous The Mathematics Department patterns — even by computer. gifts of Kirk Twiss and several holds a public lecture each April Although is mostly used by anonymous donors. The Twiss fund in conjunction with the national experienced jugglers, Knutson says provides support for the recruitment, celebration of Mathematics it’s also useful as a steppingstone retention, and research efforts of our Awareness Month. This year’s for people learning harder things. faculty. Together with other gifts, it lecture featured Professor Allen allows the department to support Knutson, who discussed the activities that are essential to our mathematics of . Professor scientific output, such as visits by Knutson joined the faculty here in preeminent mathematicians and 2009; his research interests include collaborators. algebraic geometry and algebraic The 2010 International Congress combinatorics. Until 1995, he held of Mathematicians, the quadrennial a juggling world record for world gathering of mathematicians (12 balls between two people). where Fields Medal recipients are The mathematics of juggling announced, was held this summer in was codified about 25 years ago, Hyderabad, India. Karen Vogtmann when three different groups of had the honor to chair the official jugglers came up with the same U.S. delegation to the congress and way of mathematically representing Professor Knutson’s lecture two of our faculty, Lou Billera and a juggling pattern. This notational and demonstration is available on Justin Moore, gave invited lectures. system, called “,” made CornellCast: Congratulations to Karen, Lou, and it easy to record patterns, note www.cornell.edu/video Justin! similarities, and find new juggling Visiting Ithaca By Patricia Hersh Spending fall semester of 2010 to College-town visiting the Cornell math department, for pizza for lunch thanks to the generous support of the one day. Recently I Ruth I. Michler Memorial Prize, is a visited the breath- wonderful opportunity for me. Not taking gorge and only is there the strong geometric series of cascades combinatorics group comprised leading to Lucifer of Lou Billera, Ed Swartz, and Falls in Robert H. Allen Knutson, but also numerous Treman State Park other people using combinatorics (thanks to Ravi (particularly my specialty area Ramakrishna’s of topological combinatorics) in recommendation). exciting, highly nontrivial ways: With fresh energy Irena Peeva in conjunction with just after seeing free resolutions, Ken Brown in Lucifer Falls, a connection with group theory, and collaborator and Karen Vogtmann in her work on the I made a break- space of phylogenetic trees, just to through on how to name a few. Indeed, I am learning think about a strati- Laurent Saloff-Coste, Patricia Hersh, a lot from talking with an array of fied space related to and Georgia Benkart, President of the AWM different people and have identified phylogenetic trees. a few possible joint projects with This past weekend I attended a real learning opportunity for all Cornell faculty members, still in an impressive series of talks at the involved. early stages. conference Approaches to Group It is a very nice thing that I am also finding a little time Theory honoring Ken Brown. the Michler family has done in to enjoy Ithaca. Tara Holm took Speaker after speaker made his creating this prize as a tribute to me to the farmer’s market and or her talk understandable for Ruth Michler. I can say from my then to Gimme Coffee on my first people from all different areas of own firsthand experience that this Saturday morning here. Ed Swartz math, sharing perspective on their is clearly having a very positive took me walking along the gorge areas, and making the conference impact for its recipients.

International Congress of Mathematicians By Justin Moore Every four years, there is notable recent developments in the of Geneva). Louis Billera and Justin an International Congress of field. Moore presented invited talks, Mathematicians, and in 2010 the This year the math department at representing combinatorics and Congress was held in Hyderabad, Cornell was represented at the ICM logic, respectively. Finally, Keith India. Among the highlights of this in a number of different capacities. Dennis was among those recognized event is the awarding of the Fields Karen Vogtmann was the chair of for their contribution to the project Medal, the award in mathematics the U.S. delegation to the general of digitizing the proceedings of all generally regarded as the equivalent assembly of the International of the previous congresses, dating of the Nobel Prize. To be invited to Mathematical Union (the primary back to 1893. The entire database speak at the ICM is a coveted honor, political organization associated can be accessed at: with only a handful of people chosen with the ICM). Harry Kesten from each of the major divisions of presented the Fields medal laudation www.mathunion.org/ICM mathematics to speak on the most for Stanislav Smirnov (University 2 Letter from the Chair Continued from page 3. postdoctoral and visitor program per tenure/tenure-track faculty, or the U.S. clearly demonstrates that was average in size when compared per undergraduate student. a lively postdoctoral and visitor to the top 50 departments of The university’s “2010-2015 program is an essential component mathematics. This program directly Strategic Plan” calls for Cornell to of successful departments. With impacted approximately one third be recognized worldwide as a top- few exceptions, the rule is: the of our scientific activities in terms ten university. There are no top-ten better the department, the larger the of publications and seminars. In universities without a superb depart- postdoctoral and visitor program. the last two years, this essential ment of mathematics. There are no The resources supporting these component of the scientific life well-ranked departments of math- programs are mostly internal and of the department has been cut by ematics without a lively postdoc- tied to instruction. In this way, more than 65%. Today, among the toral and visitor program. Failing to mathematics service instruction 4 top mathematics programs in recognize this undisputable reality plays an essential role in supporting the state of New York (Columbia, now is sure to have very undesirable research activities at the best Cornell, NYU, Stony Brook), our long-term effects on our department departments of mathematics. department has, by far, the smallest and our university and is the chal- Looking at our department over postdoctoral and visitor program, lenge we will be addressing for the the past ten years, one finds that our whether measured in absolute size, next several years. Fashion Statement by Laurent Saloff-Coste In the late 1970s, Bill Thurston Dai Fujiwara at the presentation three-dimensional topologies.” formulated his geometrization con- of the Miyake Collection which Jenny Barchfield from the Associated jecture for 3-dimensional manifolds. was entirely inspired by his Press writes: “The collection, in an This far-reaching conjecture states geometrization conjecture. The eye-popping rainbow of mostly that all 3-manifolds can be decom- notes accompanying the collection high-tech fabrics, riffed on the idea posed into pieces that belong to a described the Thurston theory as of oblong shapes and loops, circles short list of eight model geometries. “a comprehensive vision of eight and spirals — Thurston’s model The geometrization conjecture con- geometries that are sufficient to metaphors for the universe.” tains as a special case the famous form an ideal shape for all possible In spring 2010, the Clay conjecture made by the French Institute announced that the mathematician Henri Poincaré Millennium Prize for the (1854-1912) that the 3-sphere Poincaré conjecture was is the only closed 3-dimen- awarded to Grigoriy Perelman. sional manifold on which As he had done earlier with any loop can be retracted to a the Fields medal, Perelman point. The Poincaré conjecture refused the Millennium Prize is one of the seven Millennium of $1 million but the math- Problems for the solution ematical community cele- of which the Clay Institute brated Perleman’s astonishing established a $1 million award achievements including his in 2000. This year, in Paris, proof of the geometrization Thurston’s pioneering work conjecture at a conference was celebrated on two very held at Institut Henri Poincaré different stages. in Paris in June 2010. Of At the January 2010 Paris course, Bill Thurston was one fashion show, Bill Thurston Dai Fujiwara, Bill Thurston, & Issey Miyake Designers of the featured speakers at this appeared on stage with designer photo by Takeshi Miyamoto, all rights reserved conference. 3 Writing about Math for the New York Times by Steven Strogatz Back in seems too diffuse and also assumes perfect place to communicate math August 2009, too much math sophistication. to a wide audience. I found myself How about a series that starts with In all there were 15 , eating lunch kindergarten and walks the readers each about 1,500 words long, on with David step-by-step through numbers, topics running from pre-school (the Shipley, the addition, subtraction and all that, meaning of numbers, illustrated by editor of the and then keeps going, through a Sesame Street video) to group op-ed page algebra, geometry, calculus, the theory (by way of a problem about for The New whole curriculum that everybody mattress flipping and the Klein York Times. went through but that most people 4-group) and set theory (through We’d known each other since 2003, — himself included, he confessed the allegory of the Hilbert Hotel). I having been introduced by a mutual — never really understood? tried to focus on the ideas of math, friend, and I’d written a few op-eds I couldn’t believe it. “Are you and to show why we find the subject for him over the years since then. serious? Just grinding through the so beautiful and compelling. So when he casually invited me curriculum? It sounds so pedantic,” The audience reaction was to look him up next time I was in I said. “No, that’s really what I surprisingly appreciative, and a lot the city, I felt comfortable actually want,” he said. “You’ll find a way less snarky than what you usually taking him up on it. to make it appealing. Can you do find on the Web. Hundreds of He asked if I’d ever have time it?” I said, “I’d love to try.” readers posted comments, many to write a series about math. As it To this day, I’m still stunned of which thanked the Times for happened, spring 2010 was wide by the structure he proposed. It publishing a series about math. open, since I’d taught all my courses sounded just like the kind of logical Each of the columns made it to the for the year in the fall semester. So structure we would think of! But “most e-mailed” list. A few even his next question was, what would would anyone want to read it? reached #1, momentarily displacing a series about math look like? I The series began in late January Krugman or Kristof. suggested maybe I could try writing 2010 and ran through May. It If you ever have a chance to try about math in the real world, appeared every Monday in the something like this yourself, I’d focusing on news stories with online version of the paper. Being certainly recommend it. There is some (typically hidden) connection on the Web made it possible to a great hunger out there for math, to math, like climate change, the show videos, computer simulations, more than we realize. controversy about sampling in the color images, and to link to relevant Find links to all of the columns census, and so on. No, he said, that web sites and references. It was the on www.stevenstrogatz.com

Department Honors and Awards

As is now a tradition, the Guang (Dennis) Yang won the and Eyvindur for the clarity of his department teaching awards for junior faculty teaching award for his presentations and for his leadership 2009-2010 were announced during ability to inspire his students in both and mentoring as a head TA. our popular winter holiday party in large and small classes. Mingzhong Cai and Benjamin December. Among the graduate students, Lundell shared the Battig Award. Ravi Ramakrishna won the Benjamin Lundell and Eyvindur The Hutchinson Award went senior faculty teaching award for Pálsson share the graduate to Samuel Kolins and Mihai his ability to push students to excel student teaching award. Ben was Bailesteanu. Ri-Xiang Chen and and to achieve a deep understanding acknowledged for his commitment Ho Hon Leung received the York of mathematics. to and success in communicating Award. mathematics to a broad audience,

4 Math Majors Rural Tutoring Program by Mary Ann Huntley Seventy-two majors received Bachelor’s degrees this year. The Rural Schools Mathematics districts, and the Office of Children Honors were awarded to twenty of Tutoring Program provides and Family Services. our majors: remedial help to students in remote Emeritus faculty member Summa Cum Laude areas surrounding Ithaca. This Professor Michael Morley regularly Daniel Collins is a voluntary program in which participates in the Rural Schools Nakul Dawra faculty, graduate students, and Mathematics Tutoring Program. undergraduates provide on-site Ms. Crannell, the seventh-grade Magna Cum Laude mathematics tutoring during after- mathematics teacher at Lansing Amrish Deshmukh school hours to students at George Middle School, shared this comment Vaikath Job Jr. Republic School, Groton Middle after a tutoring session: Divya Kirti School, Lansing Middle School, Matthew Paff and Newfield Middle School. After working with Prof. Seth Matthew Weinberg George Jr. Republic School is Morley, “Johnny” came into my Stephen Wolf different from the other tutoring room the next day saying: “Ms. sites because most of the students at Crannell, I didn’t get improper Cum Laude this school live on campus. This all- fractions before, but now I OWN Tamara Dietrich-Muller boys school is made up of students them.” He was feeling really Zhidong Leong who are referred by probation or good! Cangming Liu social services departments, school Yuanhong Luo Atul Luykx More information about various outreach events Daniel Perelman from the Mathematics Department is online at: Nicholas Renegar www.math.cornell.edu/Community/community.html. Christopher Romeo Juan Sagredo Junping Shao Zeynep Soysal Cornell Mathematical Contest in Modeling Gregory Strabel by Alexander Vladimirsky

Last year, the focus of the 2,254 teams from 14 countries). Harry S. Kieval Prize Cornell Mathematical Contest in Hanrong Chen, Tiffany Low, Modeling (CMCM) was on the and Ivana Thng have designed a comparative analysis of strategies model explaining the “sweet spot” The Kieval Prize is given to an to limit the spreading of “emerald phenomenon in baseball bats. outstanding undergraduate major ash borer” insects. This problem Stephen Demjanenko, Ethan Dunn, annually. This year, it was awarded is both important and highly and Joshua Edgerton earned their jointly to Daniel Collins and relevant (with recent publications rank by modeling the spatial and Nakul Dawra. in New York Times and conferences temporal patterns in behavior of of entomologists dedicated to serial criminals. it). Twelve teams submitted The next internal CMCM contest solutions and four of them were will be held November 12-16, Please keep in touch! selected to represent Cornell in 2010. The contest is co-organized the international MCM this past by the Department of Mathematics www.math.cornell.edu February. and ORIE (and co-sponsored by Two of our teams have the Cornell Campus Store). The [email protected] attained the second highest rank winners will represent Cornell in of “Meritorious” (top 19% among the international MCM 2011.

5 Research Experience for Undergraduates by Robert Strichartz (director) The Cornell math department classical Julia sets, there is now a previous work, designed and com- has been hosting a summer theory of “differential equations.” pared methods for adaptive routing, REU program since 1994 with A major goal of this project, which determined some worst-case per- support from the National has continued over several years, formance guarantees, and obtained Science Foundation. Talented is to get more information about some promising preliminary results. undergraduates from across the the solutions to these differential The Geometric Differential country and around the world equations. The students in this Equations students worked on three come here to tackle challenging project obtained a wealth of different projects, all involving and exciting research problems. numerical data, shed light on several some type of Harnack inequalities. In the summer of 2010 a total unsolved problems, and made at These are inequalities that compare of 18 students worked in three least one surprising discovery. the solution of the heat equation at areas: Analysis on Fractals, led Students in the Optimality and different times and different points by Robert Strichartz with graduate Uncertainty group worked on the in space; they were used in the student Jason Anema, Optimality age-old problem of how to find the proof of the Poincaré Conjecture. and Uncertainty, led by Alexander optimal way to do something. (The One group worked on extending Vladimirsky with graduate student quickest driving directions? The Harnack inequalities from two- Adam Chacon (a former REU most energy-efficient trajectory for dimensional Euclidean space to the undergraduate participant) and a Mars Rover? The risk-of-detec- n-dimensional case, while another Geometric Differential Equations tion-minimizing flight-plan for a worked on the same problem, led by Xiaodong Cao with graduate spy plane?) The problem becomes but on a general manifold. The student Mihai Bailesteanu. One even harder once you add to the mix third group focused on proving of the students even worked on a the uncertainty about your environ- Harnack inequalities on warped project that bridged the first two ment, conflicting goals, and mul- spaces, which have applications in areas. tiple (competing or cooperating) theoretical physics. Students in the Analysis of participants. The students in this Next year, Prof. Strichartz’ Fractals group investigated the group worked on five determinis- Analysis on Fractals project will analogs of differential equations on tic and stochastic control projects, continue, Prof. Ed Swartz will lead fractal spaces. For certain fractals, which included theoretical, algo- a combinatorics, group and Prof. including the Sierpinski gasket, the rithmic, and numerical/experimen- Keith Dennis will direct a project in Sierpinski carpet, and some of the tal components. They extended group theory.

raduate tudents warded h s 2010 G S A P D’ Math Matters is published through the combined efforts Andrew Cameron, Estimates for solutions of elliptic partial differen- of members of the department. tial equations with explicit constants and aspects of the finite element Many thanks to Laurent Saloff- method for second-order equations Coste, Bill Gilligan, Michelle Klinger, Steve Gaarder, Brenda Timothy Goldberg, Hamiltonian Actions in Integral Kähler and Smith, Heather Peterson, Bob Generalized Complex Geometry Strichartz, Alex Vladimirsky, Justin Moore, Patricia Hersh, Gregory Muller, The Projective Geometry of Differential Operators Richard Shore, Steve Strogatz, and Mary Ann Huntley for their Matthew Noonan, Geometric Bäcklund Transformations in contributions. Homogeneous Spaces Katie Huber, Sergio Pulido Niño, Financial Markets with Short Sales Prohibition Editor ([email protected])

6 Professor Anil Nerode Honored by Richard A. Shore Professor Anil Nerode, Goldwin Nerode has had an extremely pro- Logic, Documenta Mathematica, Smith Professor in the Department ductive career in service to Cornell, Future Generation Computing, of Mathematics, received an various professional organizations, and Computer Modeling and honorary Doctor of Science degree, government and industry as well. Simulation. from his alma mater, the University He has served on a wide variety of In the realm of practical appli- of Chicago, at its June 12, 2010 college and university committees cations, Nerode was a cofounder convocation ceremony. as well as ones for several profes- of Clearsight Systems Inc. (www. The degree was presented sional organizations, other univer- clearsightsystems.com/) and a co- by his former student, Robert sities, and government agencies. inventor of the hybrid systems, I. Soare, Paul Snowden Russell Nerode has also consulted for more mathematical foundations and Distinguished Service Professor in than 25 organizations, including computational technologies that Computer Science and Mathematics the Institute for Defense Analysis, they employ for real-time imple- at the University of Chicago with Institute for Naval Studies, IBM, mentation of reactive, intelligent, the following introduction: Schlumberger, the National Science distributed controllers. He is cur- Anil Nerode is one of the Foundation, and Argonne National rently working on a wide variety of foremost experts on mathematical Laboratory. He also has served applications of the mathematics he logic and the theory of as editor of some fifteen journals, has been developing and has a num- computability. One might place among them the Journal of Symbolic ber of exciting patents in the works. him in the tradition of Leibniz, with Logic, Annals of Pure and Applied a scope of all of mathematics and a goal to understand computability and effective processes in all forms, theoretical and practical. With his A.B. and Ph.D. degrees from the era of Robert Hutchins and Marshall Harvey Stone, Nerode carried the resulting intellectual and mathematical traditions with him when he left Chicago in the 1950s, a time when the fields of mathematical logic, computability, and automata theory were in their infancy. In the subsequent decades he has done more than anyone else to bring these fields to their present state, through the power of his mathematical knowledge and his unique vision. Through his research and his mathematical descendants, Nerode has had and will continue to have a profound influence on mathematical logic and computability. While honorary degrees at Chicago are awarded primarily for scholarly achievement and impact, Anil Nerode and Robert Soare

7 310 Malott Hall Ithaca, NY 14853-4201

Mathematics Department Endowments & Gifts We are grateful to alumni, friends, and family for their The Faculty Book Endowment is dedicated to provid- generosity in supporting our endowments or providing other ing the Cornell community with access to one of the world’s gifts and donations to the department. finest collections of mathematics books and publications. The Ruth I. Michler Memorial Prize, established The Israel Berstein Memorial Fund was established by Gerhard and Waltraud Michler of Essen, Germany, in in honor of Israel Berstein, a professor in this department memory of their daughter, provides funding for the Ruth I. from 1962-1991. The memorial fund is intended to help Michler Memorial Prize of the Association for Women in young mathematicians in the field of topology. Mathematics. The awardee spends a semester here without The Logic Endowment was started with a generous gift teaching obligations. from a former Cornell undergraduate to support promising The Chelluri Lecture Series was established by Raju logic students. Chelluri’s parents in his memory. Funds are used to invite The Robert John Battig Endowment was established distinguished mathematicians to give annual lectures. by his parents after his untimely death. Robert was awarded The Michael D. Morley Senior Prize in Mathematics a January 1998 Ph.D. in mathematics. The fund provides an is presented annually to an Ithaca High School student who annual prize to an outstanding continuing graduate student has excelled in mathematics and who has demonstrated in mathematics at Cornell. originality and innovative power in mathematics. If you would like to contribute, please make your check Teaching Awards for Graduate Students and fac- payable to Cornell University, indicate the endowment, or ulty were created in 2001. Prizes are awarded to graduate that it is a gift in support of Mathematics, and send it to: students. Department of Mathematics Endowments & Gifts The Colloquium Endowment Fund was instituted to 310 Malott Hall, Cornell University invite distinguished scientists to speak at the Oliver Club Ithaca, NY 14853-4201 seminars. (See www.math.cornell.edu/~oliver/.) The Eleanor Norton York Endowment was established Gifts can also be made online at in honor of Eleanor Norton York to recognize outstanding www.giving.cornell.edu graduate students in both Astronomy and Mathematics. 8