## Edward T. Cone Concert Talk

Listen to members of the string quartet Brooklyn Rider discuss music with Institute Artist-in-Residence Derek Bermel.

Brooklyn Rider

February 5, 2011

Listen to members of the string quartet Brooklyn Rider discuss music with Institute Artist-in-Residence Derek Bermel.

David Huse

Princeton University; Member, School of Mathematics

December 17, 2010

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

Andrei Jorza

Institute for Advanced Study

December 16, 2010

To a regular algebraic cuspidal representation of GL(2) over a quadratic imaginary field, whose central character is conjugation invariant, Taylor et al. associated a two dimensional Galois representation which is unramified at l different from p outside a finite set of places. The first half of this talk concerns the crystallinity of the Galois representation at p , under a technical assumption. The second half of the talk is on recent work towards local-global compatibility (on GSp(4) and its implication for GL(2)).

Chandrashekar Khare

Institute for Advanced Study

December 15, 2010

Iwasawa developed his theory for class groups in towers of cyclotomic fields partly in analogy with Weil's theory of curves over finite fields. In this talk, we present another such conjectural analogy. It seems intertwined with Leopoldt's conjecture. This talk is related to J-P.Wintenberger's talk here earlier this year.

Larry Guth

University of Toronto; Member, School of Mathematics

December 14, 2010

Erdos conjectured that N points in the plane determine at least c N (log N)^{-1/2} different distances. Building on work of Elekes-Sharir, Nets Katz and I showed that the number of distances is at least c N (log N)^{-1} . (Previous estimates had lower bounds like N^{.86}.)

Zihua Guo

Institute for Advanced Study

December 13, 2010

We prove that the Cauchy problem for the Benjamin-Ono-Burgers equation is uniformly globally well-posed in H^1 for all "\epsilon\in [0,1]". Moreover, we show that for any T>0 the solution converges in C([0,T]:H^1) to that of Benjamin-Ono equation as "\epsilon --> 0". Our results give a new proof for the global well-posedness of the BO equation in H^1(R) without using gauge transform, which was first obtained by Tao using gauge transform, and also solve the problem about the inviscid limit behavior in H1.

Paul Seymour

Princeton University

December 13, 2010

A ``tournament'' is a digraph obtained from a complete graph by directing its edges, and ``colouring'' a tournament means partitioning its vertex set into acyclic subsets (``acyclic'' means the subdigraph induced on the subset has no directed cycles). This concept is quite like that for graph-colouring, but different. For instance, there are some tournaments H such that every tournament not containing H as a subdigraph has bounded chromatic number. We call them ``heroes''; for example, all tournaments with at most four vertices are heroes.

Edward Witten

Institute for Advanced Study

December 15, 2010

Ralph Kaufmann

Purdue University; Member, School of Mathematics

October 20, 2010

Igor Rivin

Temple University; Member, School of Mathematics

October 20, 2010

we will describe various models of sparse and planar graphs and the associated distributions of eigenvalues (and eigenvalue spacings) which come up. The talk will be light on theorems, and heavy on experimental data.