BIMSA > Research seminar in Discrete Mathematics Research seminar in Discrete Mathematics Van der Waerden numbers
Van der Waerden numbers
Organizers
Jie Ma , Benjamin Sudakov , Ruijie Xu
Speaker
Jacob Fox
Time
Tuesday, September 15, 2026 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899 (BIMSA)
Abstract
The van der Waerden number w(k;r) is the minimum positive integer N such that every r-coloring of the first N positive integers contains a monochromatic k-term arithmetic progression. The fact that these numbers exist was proved by van der Waerden a century ago and is among the pillars of Ramsey theory and additive combinatorics. Despite this, we still do not understand these numbers well. I will discuss recent developments giving improved bounds on these numbers and variants and how a variety of tools have been used in these results from combinatorics, analysis, probability, number theory, and algebra. The newest results I will discuss are in various joint works with Zach Hunter, Carl Schildkraut, Marcelo Campos, David Conlon, and Huy Tuan Pham.
Speaker Intro
Jacob Fox is a Professor in the Department of Mathematics at Stanford Unversity. Before joining Stanford in 2015, he was the faculty of the MIT Department of Mathematics. He completed his Ph.D. in mathematics at Princeton University in 2010. His advisor was Benny Sudakov. His research interests include extremal combinatorics, algebraic and probabilistic methods in combinatorics, Ramsey theory, graph theory, combinatorial geometry, and applications of combinatorics to computer science.