# Upcoming Events

In this talk, we will present a martingale based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is needed for the Hamiltonian $\inf_{u \in U} H(t,x,u, z,p)$, and stochastic optimal control problems (SOCP) with…

Abstract: It is well-known that in three space dimensions, smooth solutions to the equations describing a compressible gas can break down in finite time. One type of singularity which can arise is known as a "shock", which is a hypersurface of discontinuity across which the integral forms of…

In many situations, the combined effect of advection anddiffusion enhances dissipation. I will talk about this in two contexts: The first is for a randomly shifted alternating shear flows where we show that dissipation enhancement occurs on time scale O(\ln κ), where κ is the molecular…

Abstract

We will continue the computation of Gromov-Witten invariants on the quintic 3-fold by using the Atiyah-Bott localization method.

The main reference we will use is Chapter 9 of "Mirror Symmetry and Algebraic Geometry" by David Cox and Sheldon Katz.

Let S be a subset of the Boolean hypercube {0,1}^n that is both an antichain and a distance-r code. How large can S be? I will discuss the solution to this problem and its connections with combinatorial proofs of results in Littlewood-Offord theory.

Based on joint work with…

A major goal of additive combinatorics is to understand the structures of subsets A of an abelian group G which has a small doubling K = |A+A|/|A|. Freiman's celebrated theorem first provided a structural characterization of sets with small doubling over the integers, and subsequently Ruzsa in…

I'll discuss some recent work of Michael Christ which establishes smoothing for the integral of a four-fold product. In particular, I will outline some key ideas involving a reduction to the trilinear case using **spicy** Cauchy-Schwarz, a study of sublevel set estimates for a…

Student spectral sequences seminar.