Michael Björklund: The ergodic theory of sumsets

Additive combinatorics is concerned with the structure of sumsets in countable abelian groups. In this talk I will try to sketch a recent approach to problems in additive combinatorics via ergodic theory. Our main result is an estimate of the size of the sum of two sets in a countable abelian group when one of the sets is open in the Bohr topology, along with sharp characterizations of the end cases. The proofs demand a very good understanding of return time ergodic theorems in the spirit of Bourgain.

The talk is based on joint work with A. Fish.