Multiple correlations and nilsequences

Multiple correlation sequences first appeared implicitly in Furstenberg’s proof of Szemeredi’s theorem. Bergelson, Host and Kra later proved they can be decomposed into the sum of a nilsequence and a sequence tending to zero in density. Motivated by this, Frantzikinakis asks whether we have a similar decomposition along the sequence of primes p_n, or Hardy sequence [n^c], or 2^n. In this talk, I’ll answer this question affirmatively. Even though the positive answers to the prime and Hardy sequences are expected, the positive answer to 2^n is somewhat surprising and has an interesting connection with harmonic analysis.

Date: Jun 17, 2019 at 15:30:00 h
Venue: Beauchef 851, Torre Norte, 7mo piso, Sala de Seminarios John Von Neumann
Speaker: Anh Le
Affiliation: Northwestern University
Coordinator: Prof. Italo Cipriano

Posted on Jun 14, 2019 in Dynamical Systems, Seminars