Title: Quantitative multiple recurrence in ergodic theory
Speaker: Sebastian Donoso (Universidad de O’Higgins)
Abstract: In this talk I will survey recent development of the multiple recurrence problem in ergodic theory. For a probability spaceand measure preserving transformations , the problem is to study the largeness of the set of such that
where take integer values on the integers and is a suitable function. I will mention key results and comment on the problem for commuting transformations, linear and polynomial functions . I plan to provide some proofs that rely on combinatorial constructions.