# Past Events

Abstract: We will use the random sign matrix model to examine methods for bounding the probability that the least singular value is small. This quantity is relevant in many (and in some cases the only known) methods to establish limiting spectral laws of all sorts of random matrix models. It's…

The world teems with examples of invasion, in which one steady state spatially invades another. Invasion can even display a universal character: fine details recur in seemingly unrelated systems. Reaction-diffusion equations provide a mathematical framework for these phenomena. In this talk…

A theorem of Donaldson and Sun asserts that the metric tangent cone of a smoothable Kähler–Einstein Fano variety underlies some algebraic structure, and they conjecture that the metric tangent cone only depends on the algebraic structure of the singularity. Later Li and Xu extend this…

Suppose you wish to find a 2^n by 2^n matrix by asking this matrix question that it honestly answers. For example you can ask question ``What is your (1,1) element?’’

Obviously you will need exponentially many questions like that. But if one knows some information on Fourier side then one…

Moments of L-functions have been important in number theory and are well-motivated by a variety of arithmetic applications. The main goal of this talk is to illustrate (through examples and analogies) how the theory of period integrals can be applied to various moment problems, following the…

The stochastic heat equation is a fundamental model in statistical physics featuring noise scaled by the solution itself. In this talk, I will discuss the pointwise statistics of a family of nonlinear stochastic heat equations in the critical dimension two. Curiously, these statistics evoke a "…

The stochastic heat equation is a fundamental model in statistical physics featuring noise scaled by the solution itself. In this talk, I will discuss the pointwise statistics of a family of nonlinear stochastic heat equations in the critical dimension two. Curiously, these statistics evoke a "…

In this talk I will explain a surprising relation between mod 2 index theory and Seiberg-Witten invariants. This relation arose from my calculation of the mod 2 Seiberg-Witten invariants of spin structures. I will also discuss the proof of this calculation, which uses ideas from families Seiberg…

Abstract:

Harmonic measure is the probability that a Brownian traveler starting from the center of the domain exists through a particular portion of the boundary. It is a fundamental concept at the intersection of PDEs, probability, harmonic analysis, and geometric measure theory,…

Harmonic measure is the probability that a Brownian traveler starting from the center of the domain exists through a particular portion of the boundary. It is a fundamental concept at the intersection of PDEs, probability, harmonic analysis, and geometric measure theory, and yet most questions…