Past Events

Abstract: I will explain how the  count of algebraic curves in the complex projective plane can be reduced to a solution of a Hamilton-Jacobi equation.

We will describe recent progress, in joint work with Jeck Lim, on the study of sumset estimates in higher dimensions. The basic question we discuss is the following: given a subset A of d-dimensional space and a linear transformation L, how large is the sumset A + LA?

We will review some recent progress on the general geometric behavior of homologically area-minimizing subvarieties, namely, objects that minimize area with respect to homologous competitors. They are prevalent in geometry, for instance, as holomorphic subvarieties of a Kahler manifold, or as…

We will talk about the local L2 bounds of the Eisenstein series on the general reductive groups. First, we will discuss how the Maass—Selberg relations, when used to understand the L2 norm of an Eisenstein series, yields a complicated combinatorial problem. Second, we will discuss how the ideas…

Nonlinear resonance is a mechanism by which energy is continuously exchanged between a small number of wave modes, and is common to many nonlinear dispersive wave systems. In the context of free-surface gravity waves, nonlinear resonances have been studied extensively over the…

Abstract

A striking phenomenon in probability theory is universality, where different probabilistic models produce the same large-scale or long-time limits. One example is the Kardar-Parisi-Zhang (KPZ) universality class, which encompasses a wide range of natural models such as growth processes modeling…

TBD.

Abstract:   In a recent machine learning based study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the P-th Frobenius trace of elliptic curves of prescribed rank and conductor in an interval range. Sutherland discovered that this…