New types of symmetries have been considered in algebra and algebraic geometry and a higher analog of representation theory has been developed to answer questions of classical representation theory. Geometric representation theory can be viewed as...

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School of Mathematics

For a fixed integer k > 1, the Boolean k-XOR problem consists of a system of linear equations mod 2 with each equation involving exactly k variables. We give an algorithm to strongly refute *semi-random* instances of the Boolean k-XOR problem on n...

The physicist Abrikosov predicted that in certain superconductors, one should observe triangular lattices of vortices, now called Abrikosov lattices. When studying ground states of Coulomb gases, which is motivated by questions in approximation...

In this talk, I will give an overview of some recent results motivated by the computation and applications of persistent homology, a theory that creates a bridge between the continuous world of topology and the discrete world of data, and...

The group of Hamiltonian diffeomorphisms of a symplectic manifold admits a remarkable bi-invariant metric, called Hofer’s metric. My talk will be about a recent joint work with Dan Cristofaro-Gardiner and Vincent Humilière resolving the following...

Consider the function field F of a smooth curve over FqFq, with q>2q>2.

L-functions of automorphic representations of GL(2)GL(2) over FF are important objects for studying the arithmetic properties of the field FF. Unfortunately, they can be...

Covers chapter 8 in Jantzen's book.

A discrete countable group is matricially stable if its finite dimensional approximate unitary representations are perturbable to genuine representations in the point-norm topology. We aim to explain in accessible terms why matricial stability for a...

This talk introduces a directed analog of the classical Laplacian matrix and discusses algorithms for solving certain problems related to them. Of particular interest is that using such algorithms, one can compute the stationary distribution of a...

I will survey results related to graph comparison; graph comparison is a certain type of restriction on a metric spaces which is encoded by a given graph.