|Date: Monday, April 04, 2022
Location: 3866 East Hall (4:00 PM to 5:00 PM)
Title: Szemerédi's Regularity Lemma and its Applications
Abstract: Szemerédi's regularity lemma is a powerful statement about the randomness of large dense graphs. Roughly speaking, it says that the vertices of every large enough graph can be partitioned into a bounded number of parts so that between two parts the edges behave almost randomly. Although most commonly used as a tool in extremal graph theory, it has some elegant applications to other areas of extremal combinatorics.
In this talk, we will explore its application to Roth's Theorem, a statement about the existence of arithmetic progressions in sets with positive upper density.
Speaker: Mia Smith