Past Events
Scholze has conjectured the existence of the so-called Igusa stacks, which have close relation to Shimura varieties. In my thesis and the joint work in progress with Daniels, van Hoften and Kim, these conjectural stacks are constructed for many interesting classes of Shimura varieties. In this…
Calculus is hard. In most textbooks and calculus classes, the chain rule (f∘g)′(x) = f′(g(x))∘g′(x) is either not proved, or only partially proved. The reason is that the proof requires knowledge of topology not covered in the first two years of university, and most importantly, the result fails…
Abstract: I will introduce the GOE (orthogonal) and GUE (unitary) Gaussian ensembles, which are special Wigner matrices with Gaussian entries leading to nice symmetries. The main result will be the Ginibre formula for the density of the eigenvalues of these ensembles. There are several ways to…
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