|Location:||60 Evans Hall|
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.