## Student Working Seminar in Groups and Dynamics

**Date:** December 4, 2019

**Time:** 1:00PM - 2:00PM

**Location:** BLOC 628

**Speaker:** James O'Quinn

**Title:** *The Furstenberg-Zimmer structure theorem and a proof of Szemerédi's theorem*

**Abstract:** The Furstenberg-Zimmer structure theorem is a way to partially recover the dichotomy between weak mixing and compact vectors inherent in the study of unitary representations of groups into the p.m.p. action setting. During this talk, I will prove one version of the Furstenberg-Zimmer theorem using some measure theoretic techniques, and then show how Szemerédi's theorem follows from this result.