Disk Configuration Spaces and Topological Complexity

Explore the fascinating world of disk configuration spaces and topological complexity in this 51-minute lecture by Nick Wawrykow. Delve into the study of configuration spaces of points through the lens of topological complexity, and discover how disk configuration spaces serve as natural generalizations that incorporate both geometry and topology. Focus on the ordered configuration space of n open unit-diameter disks in an infinite strip of width w, denoted as conf(n,w). Examine the topology of this space and learn how it relates to the ordered configuration space of n points in a plane when n is at most w. Investigate the drastic differences that emerge when n exceeds w. Gain insights into the calculation of topological complexity for conf(n,w) and understand its implications in the field of applied algebraic topology.