Title : Limiting behavior of multiple ergodic averages and applications

Speaker : Andreas Koutsogiannis (Aristotle University of Thessaloniki)

Abstract : In this talk we will discuss norm-convergence results for multiple ergodic averages along sequences of polynomial growth. Combining these results with Furstenberg’s correspondence principle, we will derive several applications in combinatorics. Namely, we show that subsets of positive integers of positive upper density contain various arbitrarily long combinatorial patterns. We will also obtain far-reaching extensions to Szemerédi’s theorem, which states that any such subset of positive integers contains arbitrarily long arithmetic progressions.

Zoom Link : https://us06web.zoom.us/j/83540915663?pwd=Eu4WYFDWUxun53COoBaQmYNjwa5LaS.1