Joel Moreira

Multiple recurrence for polynomial and non-polynomial sequences

The multiple recurrence theorem of Furstenberg proved in 1977 opened the doors to many subsequent extensions establishing recurrence along a variety of sequences. The study of more general multiple recurrence results led to remarkable developments in our understanding of the structure of measure preserving systems, and has interesting applications to number theory and combinatorics. I will survey some of these developments and present a new theorem, recently obtained in joint work with Bergelson and Richter, which combines and unifies several previously known results, and implies many new ones.