Video Lectures

Khovanov showed, more than 20 years ago, that there is a deeper theory underlying the Jones polynomial. The``knot categorification problem” is to find a uniform description of this theory, for all gauge groups, which originates from physics. I found...

Mean curvature flow (MCF) is a geometric heat equation where a submanifold evolves to minimize its area. A central problem is to understand the singularities that form and what these imply for the flow. I will talk about joint work with Toby Colding...

This is the second talk in a 3-lecture series whose goal is to give background as well as a self contained proof of Chen's recent breakthrough on the KLS conjecture and slicing problem (a video of the first lecture can be found here:

https://www...

(This lecture will be self-contained.) In high dimensions, what does it look like when we take the intersection of a set of random half-spaces with either the sphere or the Hamming cube? This is one phrasing of the so-called perceptron problem...

Given an elliptic curve E, Kolyvagin used CM points on modular curves to construct a system of classes valued in the Galois cohomology of the torsion points of E. Under the conjecture that not all of these classes vanish, he gave a description for...

The talk introduces the Kazhdan-Lusztig categories of representations of affine Lie algebras

(This lecture is related to the preceding lecture, but I will try to make it self-contained as much as possible.) In this lecture I will elaborate on some of the existing mathematical approaches to the study of random CSPs, particularly involving...

In the mid 80's, Bourgain asked the following question: Is there a universal constant c>0c>0 such that every compact convex set KK in RnRn, of unit volume, must contain a slice (namely, a set of the form K∩HK∩H for some affine hyperplane HH) whose...

Consider a point particle flying freely on the torus and elastically bouncing back from the boundary of fixed smooth convex obstacles. This is the celebrated Sinai billiard, a rare example of a deterministic dynamical system where rigorous results...

I will describe recent progress in determination of asymptotic behavior in random constraint satisfaction problems, including the independent set problem on random graphs, random regular NAE-SAT, and random SAT. The results include sharp phase...