Recently Added

An Elementary Proof of Anti-Concentration of Polynomials in Gaussian Variables

Shachar Lovett
Institute for Advanced Study
February 14, 2011

Recently there has been much interest in polynomial threshold functions in the context of learning theory, structural results and pseudorandomness. A crucial ingredient in these works is the understanding of the distribution of low-degree multivariate polynomials evaluated over normally distributed inputs. In particular, the two important properties are exponential tail decay and anti-concentration.

Two Dimensional Galois Representations Over Imaginary Quadratic Fields

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)).

Ramification in Iwasawa Modules

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.

Uniform Well-Posedness and Inviscid Limit for the Benjamin-Ono-Burgers Equation

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.

Colouring Tournaments

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.