EVENT DETAILS AND ABSTRACT

Title: Some recent convergence results on non-conventional ergodic averages
Speaker: Tim Austin
Speaker Info: UCLA
Brief Description:
Special Note:
Abstract:

The phenomenon of multiple recurrence in ergodic theory occurrs when several of the images of one fixed positive-measure set under some probability-preserving transformations, indexed by the points of some finite configuration in the acting group, all overlap in a set of positive measure. Instances of this were first investigated very generally by Furstenberg, who related them to Szemeredi's Theorem in additive combinatorics and so gave a new proof of that theorem. His analysis focuses on certain `nonconventional' ergodic averages, and these have gone on to attract considerable further interest. In this talk I will discuss some recent progress in their analysis, showing how an extension of an initially-given system of commuting probability-preserving transformations can be used in a proof of the norm convergence of some such averages.