Computational topology for configuration spaces of hard disks

Configuration spaces of hard spheres (in two dimensions, hard disks) are fundamental objects in topology as well as physics. Yet so far very little is known about the topology of these spaces. I will report on joint work with G. Carlsson, J. Gorham, and J. Mason on developing computational Morse theoretic methods for understanding the topology of these spaces. Dozens of changes in topology may already be observed with five particles, suggesting intricate topology underlying liquid-solid phase transitions.