## EVENT DETAILS AND ABSTRACT

**Graduate Dynamical Systems Seminar**
**Title:** Multiple ergodic averages for flows and configurations in sets of positive density in $\mathbb{R}$

**Speaker:** Amanda Potts

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

We show the $L^2$-convergence of continuous time ergodic
averages of a product of functions evaluated at return times along
polynomials. These averages are the continuous time version of the
averages appearing in Furstenberg's proof of Szemer\edi's Theorem. For
each average we show that it is sufficient to prove convergence on special factors, the Host-Kra factors, which have the structure of a nilmanifold. We also give a description of the limit. In particular, if the polynomials are independent over the real numbers then the limit is the product of the integrals. We further show that if the collection of polynomials has "low complexity", then for every set $E$ of real numbers with positive density and for every $\delta > 0$, the set of polynomial return times for the "$\delta$-thickened" set $E_{\delta}$ has bounded gaps.

**Date:** Thursday, November 5, 2009

**Time:** 3:00pm

**Where:** Lunt 104

**Contact Person:** Daniel Visscher

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

**Contact Phone:**

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