# Past Events

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…

In the study of fluid dynamics, turbulence poses a significant challenge in predicting fluid behavior, and it remains a mystery for mathematicians and physicists alike. Recently, there has been some exciting progress in our understanding of ideal turbulence: starting from Onsager’s theorem…

The Bateman-Horn conjecture gives a prediction for how often an irreducible polynomial takes on prime values. In this talk, I will discuss the proof of Bateman-Horn for two new polynomials -- the determinant polynomial on nxn matrices and the determinant polynomial on nxn symmetric matrices. A…

Abstract: Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this talk, we introduce optimization algorithms based on quantum dynamical systems. On the one hand, we leverage the global effect of…

The Kauffman bracket skein module S(M) is an invariant of a 3-manifold M, which was independently introduced by Turaev and Przytycki as a generalization of the Jones polynomial of knots. It can be defined as a quotient of the free Z[A,1/A]-module spanned by isotopy classes of links in M modulo…