at the

American Institute of Mathematics, San Jose, California

organized by

Keith Burns, Vaughn Climenhaga, Todd Fisher, and Dan Thompson

Geodesic flows are an important class of systems, whose study mirrors the historical development of the theory of dynamical systems; many major theoretical results were obtained first for geodesic flows, before being generalized to broader classes of systems. The study of geodesic flow for a closed manifold of negative curvature is by now classical. Directions of contemporary study include weakening the hypotheses on the curvature (for example, to non-positive curvature or the assumption of no focal points), weakening the compactness assumption to allow for cusps, and weakening the assumption that the underlying space is a Riemannian manifold (we could consider e.g. a locally CAT(-1) or CAT(0) metric space). Other cases of particular interest are the geodesic flow for the Teichmuller space of quadratic differentials, and certain classes of billiard flow.

The workshop will focus on developing the dynamical theory, particularly thermodynamic formalism, in the various settings described above, building on recent breakthroughs in this area in the last few years.

The main topics for the workshop are:

- Geodesic flows on non-compact negatively curved manifolds
- Geodesic flow beyond non-positive curvature for closed manifolds
- Non-Riemannian geodesic flow and billiard flows
- Teichmuller geodesic flow

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Lyapunov exponents and nonadapted measures for dispersing billiards

by Vaughn Climenhaga, Mark Demers, Yuri Lima, Hongkun Zhang

Multifractal analysis of geodesic flows on surfaces without focal points

by Kiho Park, Tianyu Wang

Unique equilibrium states for geodesic flows on flat surfaces with singularities

by Benjamin Call, David Constantine, Alena Erchenko, Noelle Sawyer, Grace Work

Topological flows for hyperbolic groups

by Ryokichi Tanaka