#
Equilibrium states for dynamical systems arising from geometry

July 15 to July 19, 2019
at the

American Institute of Mathematics,
San Jose, California

organized by

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

## Original Announcement

This workshop will address questions of existence
and uniqueness of equilibrium states, and their statistical properties, for
dynamical systems arising from geometry, particularly geodesic flows.
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

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos