Mathematical Sciences Research Institute Annual Report for 2006-2007 I. Overview of Activities……………………………………………………........ 3 New Developments………………………………………………….. 3 Scientific Program and Workshops………………………………….. 5 Program Highlights………………………………………………….. 11 MSRI Experiences…………………………………………………… 15 II. Programs……………………………………………………………………….. 24 Program Participant List……………………………………………. 25 Participant Summary………………………………………………… 29 Publication List……………………………………………………… 30 III. Postdoctoral Placement……………………………………………………....... 35 IV. Summer Graduate Workshops………………………………………………… 36 Graduate Student Summary…………………………………………. 39 V. Undergraduate Program………………………………………………………… 40 Undergraduate Student Summary……………………………………. 41 VI. External Financial Support…………………………………………………….. 42 VII. Committee Membership……………………………………………………….. 47 VIII. Appendix - Final Reports…………………………………………………......... 49 Programs………………………………………………………………. 49 Geometric Evolution Equations and Related Topics…………... 49 Computational Applications of Algebraic Topology…………... 63 Dynamical Systems…………………………………………….. 70 Workshops……………………………………………………………… 80 Connections for Women: Computational Applications of Algebraic Topology…………………………………………….. 80 MSRI Short Course: An Introduction to Multiscale Methods….. 88 Connections for Women: Geometric Analysis and Nonlinear Partial Differential Equations…………………………... 90 Recent Developments in Numerical Methods and Algorithms for Geometric Evolution Equations….………………… 91 Lectures on String(y) Topology………………………………... 94 Introductory Workshop: New Topological Structures in Physics………………………………………………… 99 Training Program in String Topology…………………………. 104 CMI/MSRI Hot Topics Workshop: Modularity for GL(2) and Beyond………………………………………….. 108 CMI/MSRI Hot Topics Workshop: Minimal and Canonical Models in Algebraic Geometry………………………. 121 CMI/MSRI Hot Topics Workshop: Advances in Algebra and Geometry……………………………………………… 130 Summer Graduate Workshop: Data Assimilation for the Carbon Cycle………………………………………….. 140 Workshop Participant List…………………………………………….. 146 3 Annual 2006-07 Report from the Mathematical Sciences Research Institute April 2008 This annual report covers MSRI projects and activities that have been concluded since the submission of the last full report in May 2006 and the interim 2006-07 report in May 2007. New Developments The year 2006-07 saw a very rich scientific program. By August 1, 2007, MSRI was comfortably resettled in its greatly expanded quarters, financed through private fund- raising. Improvements to the older part of the building, and the acquisition of appropriate furniture and equipment continued through the year. One consequence was that the Institute could run a more robust program of workshops, often in collaboration with other organizations, since in the expanded quarters the major programs are no longer disrupted by concurrent scientific events. MSRI continues to monitor and improve the balance of non-scientific staff needed to host these scientific events. The new auditorium and expanded public facilities made it possible to accommodate much larger groups for workshops. This expanded capacity was fully utilized by the large cohorts that attended the two “Hot Topics” workshops (more on these later), the “Algebra & Geometry” workshop, and the “Critical Issues in Education” workshop. While it is too soon to detect a trend, participation in programmatic workshops appears to be significantly increasing as well, which would serve to expand the impact of MSRI’s core research programs. A significant new program that does not show up in the list below but augments the science of the programs is the Simons Biology Colloquium. The Colloquium brought four famous biologists with a mathematical bent to MSRI, each for a one week stay involving 2-4 major lectures during the spring semester of 2007: Arnold Levine, Mimi Koehl, Robert Schleif, and Sydney Brenner. The biologists had interactions, in particular, with members of the Dynamical Systems program (see below). The long-term goal is to stimulate interactions of mathematics and biology by engaging the mathematicians at MSRI with some biological problems and making the Institute better known to the biological world; this may eventually lead to other sorts of programs with more intense and programmed interactions. The Colloquium, which has substantial funding from the Simons Foundation, will continue in 2007-08. Another new area for MSRI was the involvement in Climate research, beginning with a summer graduate workshop in July 2006 (joint with the National Center for Atmospheric Research), and continuing with the "Symposium on Climate Change: From Global Predictions to Local Action" that took place in April 2007. The series will continue with a Summer School in July 2007, and is expected to lead to future activities of larger scale. 4 The following summary of demographic data can also be viewed in detail later in this report. In its 2006-07 workshops, MSRI hosted 2439 separate visits (some visitors attended multiple events). 2062 participants gave us gender data. Of these 588 or 28.5%, were females. There were 109 self-reported under-represented minorities. In its 2006-07 programs, MSRI had a total of 196 members. All but one member provided gender data. Of these, 34 or 17.4% were female. 3 members were black; there were no self-identified Hispanic/Latino or Native American members, although it should be recognized that half the members declined to state Hispanic/Latino ancestry. It should recognized that the data are “noisy.” (People choose not to fill out those spaces on the forms; for some reason they are more reluctant to specify racial and ethnic data than gender data.) We now turn to the fundamental scientific programs and workshops that make MSRI such an intensely active center. There are too many to describe in detail in this space, but a listing of topics will give an idea of what has been going on. Two types of workshops may need a little explanation: 1. “Connections for Women”. While MSRI had hosted occasional “workshops for women” in the past, it was decided last year to have a “Connections for Women” workshop at the start of every semester- or year-long program, following a suggestion from then-Trustee Joyce McLaughlin. Starting with August 2006, one of these workshops now immediately precedes every MSRI Introductory Workshop. Its goal is to increase the numbers and cohesiveness of the women in the introductory workshops and, ultimately, in the whole program. The format is simple: there are scientific lectures (to which both men and women are invited and come) and networking events (to which only the women are invited). Within these parameters, formats chosen by the organizers of Connections workshops vary widely and it is not yet clear whether one can identify a “best model,” particularly since feedback from the participants has been very positive independent of format. MSRI pays some expenses for a number of women to attend, and attendance is generally in the 15-25 range. The women attending are encouraged, and supported to a significant degree, to attend the following Introductory Workshop. It should be noted that the “Connections” workshops continue to remain controversial with some female mathematicians, including potential organizers. 2. “Hot Topics” Workshops. Instituted in 2000, these are events that are planned with little lead time -- typically just 3 or 4 months -- to focus on some rapidly developing breakthrough. MSRI has averaged about one per year, though in 2006-07 there were two. The workshops gather the super-specialists to talk with each other intensely over a week and push hard on the frontier of research. The first Hot Topics workshop was titled “GL(2) and Beyond.” It goal was to spur advances in proving modularity of objects, taking off from the fact that the past few years have seen three outstanding modularity conjectures settled in a large number of cases: Serre's conjectures on mod p Galois representations; the Fontaine-Mazur conjecture for p-adic Galois representations; and the 5 Sato-Tate conjecture for elliptic curves. The aim of this workshop was to summarize the results and techniques in these directions and to sketch out a research program that will take us from GL(2) to unitary groups of higher rank. The meeting was capped by a lecture by Robert P. Langlands in which he outlined his hopes that application of techniques of analytic number theory to the trace formula would lead to proofs of his functoriality conjectures in situations inaccessible to other available techniques. The year's second Hot Topics Workshop, “Minimal and Canonical Models”, compared the two proposed proofs of the Finite Generation of the Canonical Ring (a completion of the Mori Program, in all dimensions, and more!) in a very useful way. Scientific Program and Workshops A. Major Programs and their associated workshops: There were three major Programs for the MSRI fiscal year 2006-07, and fourteen workshops associated to them: 1. Geometric Evolution Equations and Related Topics August 14, 2006 to May 25, 2007, organized by Bennett Chow, Panagiota Daskalopoulos, Gerhardt Huisken, Peter Li, Lei Ni, and Gang Tian. The focus was on geometric evolution equations, function theory, and related elliptic and parabolic equations. With serendipitous timing, this program was positioned to capitalize on the spectacular recent work of Perelman and earlier work of Hamilton on Ricci flow relating to the Poincaré and geometrization conjectures. The year-long program focused