Homology of Sliding-Squares Configuration Spaces

Explore the fascinating world of configuration spaces in this 51-minute lecture by Hannah Alpert. Delve into the comparison between the configuration space of n ordered points in the plane and that of n ordered unit squares sliding in the plane. Discover how confining these squares to a p by q rectangle affects the rank of its degree-j homology group. Learn about the surprising growth pattern of this rank, which increases like n! rather than j! as n, j, and pq grow in constant ratio. Gain insights from the joint work of Alpert, Matt Kahle, and Bob MacPherson in this Applied Algebraic Topology Network presentation.