Mathematics Department Colloquium: Groups, probability and representations

Colloquium | March 15 | 4-5 p.m. | 60 Evans Hall

 Aner Shalev, Hebrew University

 Department of Mathematics

I will discuss recent results demonstrating interplay between group theory, probability and representation theory. These include:

1. a proof of conjectures of Gowers and Viola on mixing and communication complexity;

2. non-commutative Waring problems (joint work with Guralnick, Liebeck, O'Brien and Tiep extending classical theorems of Burnside and of Feit-Thompson);

3. a probabilistic Tits alternative for linear groups, and extensions for non-linear groups (joint work with Larsen);

4. characterizing probabilistically nilpotent groups.

The talk will be suitable for a wide audience.