Explore the fascinating world of topology in this lecture on the configuration spaces of hard spheres. Delve into key concepts such as homology, point thickness, energy potential, and computational approaches. Learn about basic theorems, jink configurations, and topological functions. Discover how topology changes and the significance of critical points in relation to disks and diameters. Gain insights from the speaker's collaborators and engage with thought-provoking questions in this comprehensive exploration of applied algebraic topology.