Seminars Sorted by Series

I will describe a connection between a classical inequality of Grothendieck and approximation algorithms based on semi-definite programming. The investigation of this connection suggests the definition of a new graph parameter, called the...

We present a 3-D vector dyadic model given in terms of an infinite system of nonlinearly coupled ODE. This toy model is inspired by approximations to the fluid equations studied by Dinaburg and Sinai. The model has structural similarities with the...

This talk is motivated by some recent work of Bourgain- rezis-Mironescu. A few years ago, they introduced an elementary way of defining the Sobolev spaces $W^{1,p}$ without making any use of derivatives. I will present their definition and some...

I will talk about some joint work with Yanyan Li which extended the Liouville type theorem of Caffarelli-Gidas-Spruck's on the Yamabe equation to the fully nonlinear case.

Kostka numbers and Littlewood-Richardson coefficients appear in the representation theory of complex semisimple Lie algebras of type A, respectively as the multiplicities of weights in irreducible representations, and the multiplicities of...

Most known smoothable simply connected 4--manifolds admit infinitely many different smooth structures (distinguished, for example, by Seiberg--Witten invariants). There are some 4--manifolds, though, for which the existence of such 'exotic'...

It will be on some constructions in the candidate category of mixed Tate Motives constructed by Bloch and Kriz.

In this talk I will discuss a joint work with Lupercio, Nevins and Uribe, in which we use motivic integration to give a theory of Chern classes for singular algebraic varieties that is birationally well-behaved (i.e., with a "stringy" flavor). The...

Let F be a finite field. The Nottingham group N(F) is the group of formal power series \{ t(1+a_1 t + a_2 t^2 + ...): a_i \in F \}or, equivalently, the group of wild automorohisms of the local field F((t)). In spite of such a simple definition, the...

Classical Teichmueller space parametrizes complex structures on a Riemann surface of genus g>1. Recently several generalized Teichmueller spaces have been defined and studied by very different approaches. Nevertheless, some of the results are...

All physical systems in equilibrium obey the laws of thermodynamics. In other words, whatever the precise nature of the interaction between the atoms and molecules at the microscopic level, at the macroscopic level, physical systems exhibit...

I will discuss various issues related to the local problem on Lie groups, the asymptotics of the return probablity, and the equidistribution of dense subgroups.

Let us fix $m$ conjugacy classes $C_1,\dots,C_m$ inside $GL(n)$. The variety of $m$-tuple of matrices such that: $$X_i\in C_i, \quad i=1,\dots,m mbox{ and } X_1\dots X_m=1.$$ is a solution of the Deligne-Simpson problem. Double affine Hecke algebras...

The Mahler measure of an n-variable polynomial P is the integral of log|P| over the n-dimensional unit torus T^n with the Haar measure. For one-variable polynomials, this is a natural quantity that appears in different problems such as Lehmer's...

The polynomial Szemeredi theorem of Bergelson and Leibman states that every integer subset with positive density contains infinitely many configurations of the form x,x+p_1(n),...x+p_k(n), where p_1,...,p_k is any fixed family of integer polynomials...

We will first discuss some results on generation of finite simple groups. Using the classification of finite simple grouops, one can prove the following results: Every finite simple can be generated by two elements and the probability that a pair of...

Expository talk on work in progress. M.Chas and D.Sullivan introduced a product on the homology of the free loop spaace of a compact, oriented manifold M that has also been studied by R.L.Cohen, V.Godin, J.D.S.Jones, J.Klein, and others. If M is...

A fake projective space is a smooth complex projective algebraic variety which is uniformized by the unit ball in $\mathbb C^n$ and whose Betti numbers are the same as that of $\mathbb P^n_{\mathbb{C}}$. The first example of a fake projective plane...

Let G be a semisimple adjoint group. There is a partition of its wonderful compactification into finitely many G-stable pieces, which was introduced by Lusztig. Each piece is a locally trivial fibration over a partial flag variety with fibres...

I'll first summarize my conjecture about the p-adic slopes of modular forms for GL_2 (both classical and overconvergent). This conjecture is based upon some structures in the geometry of the special fibers of elliptic modular curves at p. In an...

Recently, I defined an open Gromov-Witten invariant for Lagrangian submanifolds that arise as the real points of a real symplectic manifold. In this talk, I will discuss a calculation of the genus zero open Gromov-Witten theory of the Fermat type...

In this talk, I'd like to discuss an intriguing equidistribution property of automorphic forms on arithmetic quotients of homogeneous varieties, focusing on cuspidal Hecke eigenforms for Sp(n, Z), the Siegel modular group of genus n. Our approach is...

We introduce and construct the "AC geometry" from the Gaussian free field and use it to prove various facts about Schramm-Loewner evolutions. 

We introduce and construct the "AC geometry" from the Gaussian free field and use it to prove various facts about Schramm-Loewner evolutions.