# Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

## Higher Order Sumsets in Sets of Positive Density

Abstract: In this talk we present a natural generalization of a sumset conjecture of Erdos to higher orders, asserting that every subset of the integers with positive density contains a sumset $B_1+\ldots +B_k$ where $B_1, \ldots , B_k$ are infinite. 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 Kra, Moreira, and Robertson.

### Date & Time

March 02, 2023 | 11:15am – 12:15pm

### Location

Simonyi Hall 101 and Remote Access### Speakers

### Affiliation

Member, School of Mathematics