Video Lectures

Many problems from complexity theory can be phrased in terms of tensors. I will begin by reviewing basic properties of tensors and discussing several measures of the complexity of a tensor. I'll then focus on the complexity of matrix...

This talk is intended for a general audience. The recent discovery of an interpretation of constructive type theory into abstract homotopy theory has led to a new approach to foundations with both intrinsic geometric content and a computational...

Holant Problems are a broad framework to describe counting problems. The framework generalizes counting Constraint Satisfaction Problems and partition functions of Graph Homomorphisms.

We prove a complexity dichotomy theorem for Holant problems over...

This talk is part of a circle of ideas that one could call ``categorical dynamics''. We look at how objects of the Fukaya category move under deformations prescribed by fixing an odd degree quantum cohomology class. This is an analogue of moving...

To any essentially self-dual, regular algebraic (ie cohomological) automorphic representation of GL(n) over a CM field one knows how to associate a compatible system of l-adic representations. These l-adic representations occur (perhaps slightly...

The Fermionic Fokker-Planck equation is a quantum-mechanical analog of the classical Fokker-Planck equation with which it has much in common, such as the same optimal hypercontractivity properties. In this paper we construct a Riemannian metric...

35 years ago Wehrl defined a classical entropy of a quantum density matrix using Gaussian (Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other classical approximations, has the virtue of being positive. He conjectured that the...