Speaker: Professor Henry Towsner

Abstract:

I will discuss the recent proof of the Erdos Sumset Conjecture by Moreira, Richter, and Robertson: for every set of natural numbers A with positive density, there are infinite sets B and C so that the sumset B+C is contained in A.  I’ll focus on the role of “decompositions” in the proof: the proof uses two distinct notions of pseudo-randomness, and two corresponding ways of decomposing the set A into a structured contribution and a pseudo-random one.