Higher order Fourier analysis

Abstract: The purpose of this talk is to present an area where significant progress has been made in the past 15 years. This includes Gowers's breakthrough paper on Szemeredi's theorem, results by Host and Kra on characteristic factors, the hypergraph regularity method by  Rodl, Skokan, Nagle, Schacht and the famous Green-Tao theorem on prime numbers. A beautiful landscape is emerging now at the boundary of ergodic theory, Szemeredi's regularity method and higher order Fourier analysis. We present a rather general approach to the subject which is based on the Elek-Szegedy results on hypergraph regularity.