Title: Configuration Spaces of Hard Disks in a Torus
Speaker: Katherine Ritchey (Ohio State University)
Abstract: In this talk, we’ll look at how computational methods can be used to better understand the topology of configuration spaces of non-overlapping hard disks of equal radius in a 60-degree flat torus. We would like to understand the topology of the configuration space as the radius changes. There is motivation to study such configuration spaces since it is the natural generalization of the configuration space of points in the torus. Additionally, hard disks are studied as a simple model of matter in statistical mechanics, and computer simulations suggest that the disks undergo phase transitions, so there is motivation to study the underlying topology from a physics perspective as well. Not much is currently known about such configuration spaces, but a result by Yuliy Baryshnikov, Peter Bubenik, and Matthew Kahle shows that the topology of these configuration spaces can only change at “critical,” or mechanically balanced, configurations. We’d therefore like to have a better understanding of the critical configurations that can arise in the torus. In this talk, I will discuss what is currently known about such configuration spaces, as well as computational experiments performed to find critical configurations in the torus for small numbers of disks. I will also describe methods used to classify the symmetries of the critical configurations and some ways to find new critical configurations from existing critical configurations.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html