Analysis Seminar

Four years ago a connection was made between quantitative bounds for polynomial progressions in sets of integers of positive density and quantitative bounds for multilinear, polynomial ergodic averages. We have now identified an estimate which lies at the heart of both these problems. This inequality can be viewed in a variety of ways but for harmonic analysts, it is simply a Sobolev smoothing estimate for multilinear averages in the integers. In this talk, I will describe this connection in the context of the primes. This is joint work with Mariusz Mirek and Renhui Wan.