Bryna Kra : Nilsystems in dynamics

Posted by , part of the Departmental Colloquium.

At

Nov. 6, 2009, 3 p.m.

In

SEO 636

Abstract

The connection between ergodic theory and additive combinatorics dates back to the 1970's, with Furstenberg's proof of Szemeredi's Theorem via ergodic theory. Certain algebraic constraints (arising from nilsystems) play a key role in understanding objects that arise in Furstenberg's proof. More recently, nil-structures have been imported into the finite combinatorial setting, playing a role in finding patterns in the primes. I will give an overview of where nilsystems arise in ergodic theory and topological dynamics, explaining some of the connections to additive combinatorics.