I will describe some recent advances in the study of infinite and finite groups, related to probability, growth and complexity. I will start with the celebrated Tits alternative for linear groups, and present extensions and variations, including a joint work with Larsen on a probabilistic Tits alternative. This is related to the notion of probabilistic identities, and related results and open problems will be mentioned. I will then discuss approximate subgroups, an important result by Breuillard-Green-Tao and Pyber-Szabo, and some new growth results with Liebeck and Schul. Finally I will describe recent work of Gowers and Viola on communication complexity, and present extensions and solutions to some of their conjectures. The talk will be accessible to a wide audience.
Thu, 19/05/2016 - 14:30 to 15:30
Manchester Building (Hall 2), Hebrew University Jerusalem