Video Lectures

Near-Earth space has become increasingly valuable and its use for civil (e.g., scientific), commercial, and military purposes has grown enormously in recent years. This growth has been driven in part by a rapid decrease in space-launch costs, which...

The zeta-instanton equation (also known as Witten's d-bar equation) is a partial differential equation arising in two-dimensional supersymmetric field theory. In this talk I will review some of its properties and applications, from the...

The unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of SL2(ℤ) whose Fourier coefficients have bounded denominators must be a modular form for some congruence...

Although today’s nuclear arsenals are not much in the news, they pose enormous risks for all humanity. Moreover, many treaties that have reduced the threat of nuclear weapons are now being abandoned, and enormous resources are scheduled to be spent...

Given a finite graph, the arboreal gas is the measure on forests (subgraphs without cycles) in which each edge is weighted by a parameter β>0. Equivalently this model is bond percolation conditioned to be a forest, the independent sets of the...

 I will explain how the conformal bootstrap can be adapted to place rigorous bounds on the spectra of automorphic forms on locally symmetric spaces. A locally symmetric space is of the form H\G/K, where G is a non-compact semisimple Lie group, K the...

Somehow, despite the title, SL(2,Z) is the poster child for arithmetic groups not satisfying the congruence subgroup property, which is to say that it has finite index subgroups which can not be defined by congruence conditions on their coefficients...

In these two talks, I will describe how the classification of locally homogeneous geometric structures (closely related to flat connections) leads to interesting dynamical systems.

Many interesting dynamical systems arise from the classification...

I will present an elementary introduction to the regularity/uniqueness issues for the Navier-Stokes equations. Thanks to the convex integration technique, the h-principle is starting to take shape for the uniqueness problem. It might be possible...