Inspiring John von Neumann Lecture by Lisa Sauermann

On 17 October, Prof. Dr. Lisa Sauermann (University of Bonn) gave the "John von Neumann Lecture" at Mathematics Münster. Many researchers joint her inspiring talk "On three-term progression-free sets and related questions in additive combinatorics" and the reception in the Common Room of the Cluster of Excellence afterwards.

Abstract:
Given some large positive integer \( N \), what is the largest possible size of a subset of \( \{1, \ldots, N\} \) which does not contain a three-term arithmetic progression (i.e., without three distinct elements \( x, y, z \) satisfying \( x + z = 2y \))? Similarly, given a prime \( p \) and a large positive integer \( n \), what is the largest possible size of a subset of the vector space \( \mathbb{F}_p^n \) which does not contain a three-term arithmetic progression? This talk will explain the known bounds for these longstanding problems in additive combinatorics, give an overview of proof techniques, and discuss their applications to other additive combinatorics problems.

About Lisa Sauermann
Lisa Sauermann is a German mathematician specializing in extremal and probabilistic combinatorics. She held positions at Stanford, the Institute for Advanced Study in Princeton, and was an assistant professor at MIT before accepting a Hausdorff Chair at the University of Bonn in 2023. Her numerous awards include the Richard-Rado Preis, the European Prize in Combinatorics and the von Kaven Preis of the DFG.

Link:
John von Neumann Lecture