EVENT DETAILS AND ABSTRACT

Title: Nilsequences and multiple correlations along subsequences.
Speaker: Anh Le
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Let $(X, \mu, T)$ be a measure preserving system and $f$ a bounded function on $X$. The sequence $a(n) = \int f T^n f ... T^{kn} f d \mu$ is called a multiple correlation sequence. By the works of Bergelson, Host, Kra and Leibman, a multiple correlation sequence can be decomposed into a sum of a nilsequence (a sequence defined by evaluating a continuous function along an orbit in a nilsystem) and a nullsequence (a sequence that is zero in uniform density). In this talk, we present a refinement of that result by showing the nullsequence is null along primes, along integer polynomials and Hardy field sequence $[n^c]$.