Wednesday 16 March from 12:00–13:00 in Carslaw 535A

Twisted multiple recurrence and patterns in large sets

Kamil Bulinski (Sydney)

Abstract

Recurrence is a fundamental notion in Ergodic Theory and Dynamical systems. It has a strong relationship with combinatorial number theory, as was first shown by Furstenberg when he proved a multiple recurrence result to deduce Szemeredi's theorem on arbitrarily long arithmetic progressions in dense subsets of the integers. After demonstrating some classical recurrence results and their arithmetic corollaries, I will present some new “twisted” multiple recurrence results obtained with Björklund and their applications to images of large sets under quadratic forms. The proofs rely on Ergodic theorems for random walks on certain arithmetic lattices established by Benoist-Quint.