## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**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 $[n^c]$.

**Date:** Tuesday, April 03, 2018

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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