"Configuration spaces of hard spheres"

Matt Kahle
Ohio State University

Monday, April 23, 2012
4:00 pm
845 Patterson Office Tower

Abstract:

Configuration spaces of n points in a region of R^d are well studied in algebraic topology, and their topology is well understood. But much less seems to be known when the points actually have some thickness. These kinds of spaces also have intrinsic interest in physics, as the phase space for a hard spheres gas.

I will report on some preliminary progress on understanding the topology of these spaces. In joint work with Baryshnikov and Bubenik, we develop some theoretical tools, and in joint work with Carlsson, Gorham, and Mason, we explore these spaces computationally and see that they can be quite complicated. We see enough structure to make rough conjectures about what happens for large numbers of particles.