Seminars Sorted by Series

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. 

A very long random walk, seen from so far away that individual steps cannot be resolved, is the continuous random path called Brownian motion. This is a rough statement of Donsker's theorem and it is an example of how models in statistical mechanics...

I will report on a the following work in progress. Let X be a smooth connected curve over an algebraically closed field. Consider the dual pair H=SO_{2m}, G=Sp_{2n} over X with H split. Let Bun_G and Bun_H be the stacks of G-torsors and H-torsors on...

Color Coding is an algorithmic technique for deciding efficiently if a given input graph contains a path of a given length (or another small subgraph of a certain type). It illustrates well the phenomenon that probabilistic reasoning can be helpful...

Random waves have been investigated since the 1940's in connection with modeling telephone signals (Rice), to model sea waves (Longuet-Higgins), and since the 1970's by Berry and others to model quantum wave-functions of classically chaotic systems...

Motivated by some recent progress in the study of concentration phenomena for singularly perturbed elliptic nonlinear equations and the analogies with some problems in geometric analysis, we prove existence of new entire solutions of the focusing...

The Lubotzky-Sarnak Conjecture asserts that the fundamental group of a finite volume hyperbolic manifold does not have Property \tau. Put in a geometric context, this conjecture predicts a tower of finite sheeted covers for which the Cheeger...

What is the least surface area of a shape that tiles Rd under translations by Zd? Any such shape must have volume 1 and hence surface area at least that of the volume-1 ball, namely (–d). Our main result is a construction with surface area O(–d)...

Bose-Einstein condensation was predicted by Einstein in 1925 and was experimentally discovered 70 years later. This discovery was followed by a flurry of activity in the physics community with hundreds of papers published every year and with...

Trace formulae and relative trace formulae can be used to study the rich geometry of locally symmetric spaces. I will explain some illustrative examples coming from unitary groups in this talk.

This talk is intended for a general audience. We define and discuss a spectral invariant of closed Riemannian surfaces, namely the zeta regularized trace of inverse of the Laplacian. Physically this corresponds to the sum of squares of the...

(Joint work with Shiri Artstein-Avidan). We discuss in the talk an unexpected observation that very minimal basic properties essentially uniquely define some classical transforms which traditionally are defined in a concrete and quite involved form...

A pseudo-hermitian structure in 3-D is a contact form and an almost complex structure on the kernel of the contact form. There is a natural notion of area and mean curvature for a surface in such a geometry. I will discuss some work on the structure...

The classical isoperimetric inequality in Euclidean space asserts that among all sets of given Lebesgue measure; the Euclidean ball minimizes surface area. Using a suitable generalization of surface area, isoperimetric inequalities may be...

We will survey the role played by some classes of higher order integral conformal invariants in conformal geometry which include the integral of Q-curvature and those related to the Gauss-Bonnet integrand. We will also discuss a class of integral...