Topic: KAM Theorem and Quantum Field Theory November 18

Presenter: Antti Kupiainen, University of Helsinki

Topic: On the size of complete minimal surfaces November 18

Presenter: Nikolai Nadirashvili, University of Chicago

Topic: MAXCUT in triangle-free graphs November 19

Presenter: Noga Alon, IAS and Tel Aviv University

Abstract: We obtain sharp bounds for the minimum possible size of a maximum cut in triangle-free graphs with m edges.

These are derived by combining probabilistic techniques with algebraic tools and character-sum estimates, and improve

previous results of various researchers.

Topic: Random products of matrices, sharp ergodic theorems, and distributing November 19

points uniformly on measure spaces

Presenter: Yehuda Shalom, Princeton University

Topic: An application of Kostant's work on Lie algebra cohomology November 19

to a problem in astronomy

Presenter: Persi Diaconis, Stanford University

Abstract: Statistical analysis of red shift data leads to the problem of generating random permutations with restricted

positions. For one common censorship pattern the problem can be solved using Hanlon's adaption of Kostant's seminal

work on Lie algebra cohomology. For other censorship patterns new methods are required.

This is joint work with R. Graham.

Topic: Symplectic surfaces in a fixed homology class November 19

Presenter: R. Fintushel, Michigan State University

Topic: TBA November 19

Presenter: Jean Bourgain, Institute for Advanced Study

Topic: Period functions associated to Maass waveforms and spectral theory November 19

on the modular surface

Presenter: John Lewis, Framingham State College

Topic: Uniqeness of Kahler-Ricci solitons November 20

Presenter: Gang Tian, MIT

Topic: The conjugacy problem in the braid groups November 23

Presenter: Joan Birman, Barnard College/Columbia University

Abstract: The word and conjugacy problems in Artin's braid group were solved in 1968 in a seminal paper by F. Garside. His algorithm for the word problem was shown by W. Thurston to be polynomial in both braid index and word length,

however the complexity of the related conjugacy algorithm proved elusive. Recently, Ko and Lee and I found improvements in the Garside approach which simplify the conjugacy algorithm. The goal of my talk will be to explain our contributions and to describe the remaining problems, which are closely related to the combinatorics of the symmetric group.

Topic: On Cartan's Estimate for Matrix Valued Analytic Functions November 23

Presenter: Michael Goldstein, Toronto

Topic: An Introduction to Quantum Coding Theory November 23

Presenter: Eric M. Rains, Information Sciences Research Center AT&T Labs--Research

Abstract: One of the major difficulties in building useful quantum computers (computers which use the laws of quantum

mechanics to perform computations faster than we know how to do classically) is that such computers are inherently

analog, and thus much more susceptible to noise than classical computers. Indeed, until Peter Shor's discovery in early

1994 of the first quantum code, it was commonly believed that this problem of noise was intractable. I'll explain why

quantum codes can't exist (:-)), give some examples, and then explain the framework (additive codes over GF(4)) in

which nearly all known quantum codes can be constructed. Time permitting, I will touch briefly on some other topics

(nonadditive codes, upper bounds, open problems).

Topic: Non-uniform lattices on uniform trees November 24

Presenter: Lisa Carone, Harvard University

Topic: Zeros of Graph-counting Polynomials November 25

Presenter: David Ruelle, I.H.E.S., France

Topic: TBA November 30

Presenter: Michael Koluntzakis, Urbana-Champaign

Topic: Statistical Mechanics and the Eigenvalue Density of Random Matrices December 2

Presenter: Michael Kiessling, Rutgers University

Topic: Determinantal formulas for the correlation functions and the infinite December 3

symmetric group

Presenter: A. Borodine, University of Pennsylvania

Topic: TBA December 3

Presenter: Haim Brezis, Rutgers University and Universite Paris VI

Topic: Gauge Theory, TQFT's, and the Braid Groups December 3

Presenter: H. Elmar Winkelnkemper, University of Maryland

Topic: Integrability and selection in non-linear interface dynamics December 9

Presenter: Mark Mineev-Weinstein, Los Alamos National Laboratory

Topic: TBA December 10

Presenter: John Morgan, Columbia University

Topic: TBA December 17

Presenter: Yanyan Li, Rutgers University

Topic: TBA December 17

Presenter: Tamas Hausel, Institute for Advanced Studies