Configuration Spaces of Hard Squares

Explore the intriguing world of configuration spaces in this 59-minute lecture by Matthew Kahle. Delve into the topology of configuration spaces of points in the plane and discover the challenges that arise when introducing positive thickness to points in confined regions. Learn about recent advancements in understanding configuration spaces of hard squares within a rectangle, with a focus on quantifying the factorial rate of growth of Betti numbers. Gain insights from Kahle's collaborative work with Hannah Alpert and Robert MacPherson, as he presents their main findings and discusses the implications for the field of applied algebraic topology.