Seminar 03.24.22 Koutsogiannis – In person

Title: Convergence of polynomial multiple ergodic averages for totally ergodic systems

Speaker: Andreas Koutsogiannis – Aristotle University of Thessaloniki (Greece)

Abstract: A collection of integer sequences is jointly ergodic if for every ergodic measure preserving system the multiple ergodic averages, with iterates given by this collection of sequences, converge to “the expected limit” in the mean, i.e., the product of the integrals. Exploiting a recent approach of Frantzikinakis, which allows one to avoid deep tools from ergodic theory that were previously used to establish similar results, we study joint ergodicity in totally ergodic systems for integer parts of real polynomial iterates. More specifically, our main results in this direction are a sufficient condition for k terms, and a characterization in the k=2 case. Joint work with Wenbo Sun.