Lecture by Matthew Kahle (Ohio State University): Configuration spaces of hard disks in an infinite strip

May 20, 2019 | 02:15 PM

This is joint work with Bob MacPherson. We study the configuration space config(n,w) of n non-overlapping disks of unit diameter in an infinite strip of width w. Our main result establishes the rate of growth of the Betti numbers for fixed j and w as n → ∞. We identify three regions in the (j,w) plane exhibiting qualitatively different topological behavior. We describe these regions as (1) a “gas” regime where homology is stable, (2) a “liquid” regime where homology is unstable, and (3) a “solid” regime where homology is trivial. We describe the boundaries between stable, unstable, and trivial homology for every n ≥ 3.

Time & Location

May 20, 2019 | 02:15 PM

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
Room MA 041 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)