Norm and pointwise averages of multiple ergodic averages and applications

ABSTRACT: Via the study of multiple ergodic averages for a single transformation, Furstenberg, in 1977, was able to provide an ergodic theoretical proof of Szemerédi’s theorem, i.e., every subset of natural numbers of positive upper density contains arbitrarily long arithmetic progressions. We will present some recent developments in the area for more general averages, e.g., for multiple commuting transformations with iterates along specific classes of integer valued sequences. We will also get numerous applications of the aforementioned study to number theory, as we will present the corresponding results along prime (and shifted prime) numbers, topological dynamics and combinatorics. Finally, we will present a result to the most general, and far more difficult case of pointwise convergence along special sublinear functions. This is part of independent, as well as joint work with D. Karageorgos (norm case); and S. Donoso and W. Sun (pointwise case).

Date: Jul 05, 2018 at 16:30 h
Venue: Beauchef 851, Torre Norte, 7mo piso, Sala de Seminarios John Von Neumann.
Speaker: Andreas Koutsogiannis
Affiliation: The Ohio State University
Coordinator: Prof. Italo Cipriano
Abstract:
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Posted on Jun 27, 2018 in Dynamical Systems, Seminars