Speaker: Joel Moreira (Ohio State)

Title: Non-linear monochromatic patterns in N via topological dynamics

Abstract: Since Furstenberg’s seminal paper in 1977 providing an ergodic theoretic proof of Szemeredi’s theorem on arithmetic progressions, dynamical systems methods have been a very successful tool in obtaining combinatorial results. A central problem in Ramsey theory is to understand and classify which polynomial patterns can be found “monochromatically” in any arbitrary finite coloring of the natural numbers. In particular, the question of whether any finite coloring of the natural numbers yields a monochromatic pattern of the form {x+y,xy} has remained unanswered for several years. In this talk I will investigate dynamical approaches to this and related questions, employing techniques from topological dynamics.