Title: Limiting behavior of multiple polynomial averages
Speaker: Andreas Koutsogiannis (Ohio State University)
Abstract: The study of the norm limiting behavior of multiple ergodic averages has been of great importance in the area of ergodic theory. A central result, Szemerédi’s theorem (i.e., every subset of natural numbers of positive upper density contains arbitrary long arithmetic progressions) follows by a classical result on multiple ergodic averages due to Furstenberg. In this talk we will mainly deal with averages along integer part of special families of real polynomials, for a single transformation (recent joint work with D. Karageorgos) as well as for multiple commuting transformations; we will refer to results along other integer valued sequences mainly due to Bergelson, Knutson, Leibman, Chu, Frantzikinakis, Host and Kra. We will also sketch how to obtain by the aforementioned results, the corresponding results along prime numbers.