Locally CAT(-1) spaces are geodesic metric spaces satisfying a metric notion of negative curvature. These spaces are not necessarily manifolds, covering examples such as graphs equipped with an interior metric, yet they still have a geodesic flow defined on them.

We discuss recent advances in understanding the dynamical properties of these geodesic flows via symbolic dynamics. We obtain results which extend the analogy with the negative curvature Riemannian setting. This is joint work with Dave Constantine and Jean-Francois Lafont. Speaker(s): Dan Thompson (The Ohio State University)