# Past Events

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…

Abstract

We introduce a new way to look at level sets of eigenfunctions by viewing the value of the eigenfunction as an independent time variable, with successive level surfaces evolving over time. The evolution obeys a variational principle analogous to mean curvature flow, and this…

Monstrous Moonshine was initiated by an observation relating the largest sporadic finite simple group to supersingular elliptic curves. We will explain how a closer look at the geometric side of this coincidence leads, via K3 surfaces, to a role for the smallest sporadic finite simple group…

Studying symplectic structures up to deformation equivalences is a fundamental question in symplectic geometry. Donaldson asked: given two homeomorphic closed symplectic four-manifolds, are they diffeomorphic if and only if their stabilized symplectic six-manifolds, obtained by taking products…