School of Mathematics

This talk will be an exposition of a recent paper of Bezrukavnikov-Gaitsgory-Mirkovic-Riche-Rider giving an Iwahori-Whittaker model for the Satake category. The main point is that their argument works for modular coefficients. I will give some...

A sofic approximation to a countable discrete group is a sequence of finite models for the group that generalizes the concept of a Folner sequence witnessing amenability of a group and the concept of a sequence of quotients witnessing residual...

The modular representation theory of a finite group naturally breaks into different pieces called blocks, and the defect of a block is a sort of measure of its complexity. I will recall some basic aspects of this theory, and then give the complete...

Motivated by some work of Thurston on defining a Teichmuller theory based on best Lipschitz maps between surfaces, we study infinity-harmonic maps from a manifold to a circle. The best Lipschitz constant is taken on on a geodesic lamination...

There are striking analogies between topology and arithmetic algebraic geometry, which studies the behavior of solutions to polynomial equations in arithmetic rings. One expression of these analogies is through the theory of etale cohomology, which...

Suppose we have a cancellative binary associative operation * on a finite set X. We say that it is delta-associative if the proportion of triples x, y, z such that x*(y*z) = (x*y)*z is at least delta.

Gowers and Long studied somewhat associative...

We first describe mathematical foundation of DSGRN (Dynamic Signatures Generated by Regulatory Networks), an approach that provides a queryable description of global dynamics of a network over its entire param- eter space. We describe a connection...

DNA rearrangement is observed at developmental and evolutionary scale. The recombination process can be directly modeled by 4-regular graphs and Gauss codes, also called double occurrence words. We discuss properties of these graphs, their spatial...

Following Bourgain, Gamburd, and Sarnak, we say that the Markoff equation x2+y2+z2−3xyz=0 satisfies strong approximation at a prime p if its integral points surject onto its Fp points. In 2016, Bourgain, Gamburd, and Sarnak were able to establish...

This is the last talk towards understanding Bezrukavnikov-Finkelberg's derived geometric Satake equivalence. With the preparations from previous talks, we will introduce two filtrations: a topological filtration on the equivariant cohomology and an...