Recent advances on multiple ergodic averages

RESUMEN      In 1977, Furstenberg gave a dynamical proof of the theorem of Szemerédi on the existence of arithmetic progressions in dense subsets of integers. In doing so, he initiated the use of ergodic methods to solve problems originating from additive combinatorics and number theory. A central object of study in this field are multiple ergodic averages, a class of multilinear operators that generalize classical Birkhoff averages and can be used to count the number of arithmetic patterns in dense sets of integers. In this talk, I will outline the history of multiple ergodic averages, with the emphasis on the most recent developments.

Posted on Nov 21, 2025 in Dynamical Systems, Seminars