FoCM 2014 conference

Workshop B2 - Computational Topology and Geometry

December 15, 17:00 ~ 17:25 - Room A22

## Configuration spaces of hard disks in an infinite strip

### Matthew Kahle

### Ohio State University, United States - mkahle@math.osu.edu

We study the configuration space $C(n,w)$ of $n$ non-overlapping unit-diameter disks in an infinite strip of width $w$. We present an asymptotic formula for the $k$th Betti number of $C(n,w)$, for fixed $k$ and $w$ as $n \to \infty$. We find that there is a striking phase transition: for $w > k$ the $k$th homology is stable and is isomorphic to the $k$th homology of the configuration space of points. But for $w \le k$, the $k$th homology is wildly complicated, growing exponentially fast with $n$.

Joint work with Robert MacPherson (Institute for Advanced Study).