Title: On the limiting behavior of multiple ergodic averages
Speaker: Andreas Koutsogiannis
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.Date: Tuesday, January 16, 2018
In this talk we will mainly deal with the norm limiting behavior of 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 value sequences mainly due to Bergelson, Chu, Frantzikinakis, Host, Kra and Leibman; and also talk about a recent (joint work with S. Donoso and W. Sun) pointwise result along sublinear functions.
If time permits we will also sketch how to obtain by the aforementioned results, the corresponding results along prime (or shifted prime) numbers.