Video Lectures

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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...

A fascinating feature of some gapped systems is topological order, where the system flows to a nontrivial TQFT in the infrared. The gap is often essential to the description of these phases, so it is interesting to ask what happens to them when the...

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...