One of the fundamental questions in ergodic theory is to classify the sequences of integer times along which the ergodic theorems hold. Motivated by Bourgain’s return times theorem, Donoso, Maass, and Arya-Saavedra recently studied ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems. In this talk, we show that their results can be extended to multiple ergodic averages for commuting transformations, as well as to a broader class of sequences.

This talk is based on joint work with Sebastián Donoso, and Vicente Saavedra-Araya.