Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## On a sumset conjecture of Erdos and its generalizations

Talk by Dr. Florian Richter

**Date:** 02.05.22 **Time:** 14.05 - 15.05 **Room:** ETH HG G 43

In this talk we will investigate the question -- based on problems attributed to Erdos -- of whether every subset of the integers with positive density contains a sumset B_1+...+B_k where B_1,...,B_k are infinite sets. We will present a purely ergodic-theoretic approach to this topic. Our method relies on a newfound connection between k-fold sumsets in the integers and return times of orbits in k-fold joinings of measure preserving systems arising from the Host-Kra structure theory. This talk is based on joint work with Bryna Kra, Joel Moreira, and Donald Robertson.