Video Lectures

I will explain how to realize a gapped Hamiltonian for a (1+1)d system on the lattice which has a categorical symmetry given by the modules of the 4-dimensional Taft algebra. This category is finite but not a fusion category, a fact that presents...

In the late 1800s, in the course of his study of classical problems of number theory, the young Hermann Minkowski discovered the importance of a new kind of geometric object that we now call a convex set. He soon developed a rich theory for...

The satisfiability problem for Constraint Satisfaction Problems (CSPs) asks whether an instance of a CSP has a fully satisfying assignment, i.e., an assignment that satisfies all constraints. This problem is known to be in class P or is NP-complete...

We explore the construction of non-Weinstein Liouville geometric objects based on Anosov 3-flows, introduced by Mitsumatsu, in the generalized framework of Liouville Interpolation Systems and non-singular partially hyperbolic flows. We discuss the...

Equivariant cohomology was introduced in the 1960s by Borel, and has been studied by many mathematicians since that time.  The talks will be an introduction to some of this work.  We will focus on torus-equivariant cohomology (as well as Borel-Moore...

The reverse Khovanskii-Teissier inequality is a three term inequality for nef divisors which first appeared in the context of Kähler geometry. It provides an upper bound on a product of two divisors in terms of products with the third, hence its...

Equivariant cohomology was introduced in the 1960s by Borel, and has been studied by many mathematicians since that time.  The talks will be an introduction to some of this work.  We will focus on torus-equivariant cohomology (as well as Borel-Moore...

Extremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically, the spectral gap—the difference between the largest and second-largest eigenvalues—measures the expansion properties of a...

This talk is about the study of the Boltzmann equation in the diffusive limit in a channel domain 𝕋2×(−1,1) nearby the 3D kinetic Couette flow.  We will begin the talk with a substantial introduction for non-experts.  Our result demonstrates that...

The growth of an autonomous Hamiltonian flow in Hofer's metric is not yet well understood. A result of Polterovich and Rosen shows that generically this growth is asymptotically linear, and in all known cases where it is not, it appears to be...