# Past Events

Abstract: Compressible Euler solutions develop jump discontinuities known as shocks. However, physical shocks are not, strictly speaking, discontinuous. Rather, they exhibit an internal structure which, in certain regimes, can be represented by a smooth function, the shock profile. We…

While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as log-concavity. I will explain a new approach to proving confinement (e.g., variance upper bounds) for high-dimensional unimodal…

In this talk, I will explain how to use (relative) recursion relations in the HOMFLYPT-skein to study skein-valued open Gromov-Witten partition functions as defined by Ekholm and Shende. As a first application, I will prove a crossing formula for partition functions of basic holomorphic disks…

A fundamental problem in the arithmetic of varieties over global fields is to determine whether they have a rational point. As a first effective step, one can check that a variety has local points for each place. However, this is not enough, as many classes of varieties are known to…

Complexity theory is an interesting subject. I will show you the fastest¹ algorithm for any² problem, as well as how to compute anything³ using only three bits of memory.⁴ If time permits, I will explain why these are (at least somewhat) useful.

Abstract

I plan to cover Newman-Piza's theorem that in two dimensions, the FPP passage time T(0, x) has super-constant fluctuation (subject to some assumptions about the weight distribution). I will follow the original paper of…

I will talk about the analytic aspects of black holes, especially waves and stability questions, particularly in the context of Kerr-de Sitter spaces (positive cosmological constant).

We will discuss applications of the clean composition calculus.

In this talk, I will explain why fractional (or nonlocal) minimal surfaces are ideal objects to which min-max methods can be applied on Riemannian manifolds. After a short introduction about these objects and how they approximate minimal surfaces, I will present a vision for the future on how to…