Video Lectures

This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed.
One of the main goals for the special year on univalent foundations is the development of a logical formalism, called homotopy type theory...

Polynomial Identity Testing (PIT) is the problem of identifying whether a given algebraic circuit computes the identically zero polynomial. It is well-known that this problem can be solved with small error probability by testing whether the circuit...

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...