Speaker: Ryo Moore, Southern University of Science and Technology

Title: Multiple ergodic averages along return times

Abstract: Study of multiple ergodic averages emerged in the 70's when H. Furstenberg provided an ergodic theoretic proof of Szemerèdi's Theorem. On the other hand, study of return times averages was initiated by A. Brunel in his PhD thesis from the 60's, where one considers an ergodic average along return times of an orbit from another system.

In this talk, we will briefly survey these ergodic averages, and discuss some of the results where they intersect. In particular, we will discuss the speaker's joint work with I. Assani on showing that the sequence appearing in J. Bourgain's double recurrence theorem is a good universal weight for multiple ergodic averages in norm convergence. No prior knowledge on ergodic theory will be assumed from the audience.