at the

American Institute of Mathematics, Palo Alto, California

organized by

Fanny Kassel, Athanase Papadopoulos, Kasra Rafi, and Jing Tao

This workshop, sponsored by AIM and the NSF, will be devoted to recent developments and new directions in Teichmüller theory from the point of view of Thurston's Lipschitz metric. Originally introduced by Thurston in an unpublished manuscript in 1986, the Lipschitz metric is an "asymmetric metric" on Teichmüller space. The geometry of this metric is very rich, as Thurston showed in his paper; it relates to Finsler geometry, to the theory of measured laminations and foliations, and to the curve complex.

Interest in the Lipschitz metric has recently surged on several fronts. For instance, interesting connections have been made with other metrics on Teichmüller space, with Culler-Vogtmann's Outer space, and with three-dimensional Lorentzian geometry. One of the goals of this workshop will be to bring together mathematicians working on various aspects of the subject who do not usually meet to gather and exchange information, compare and work on open problems, learn each other's techniques, and possibly open up some new fields of study. The main topics for the workshop will be:

- Large-scale geometry of the Lipschitz metric
- Dynamics on Teichmüller space, existence of a geodesic flow for the Lipschitz metric
- Symmetrizations of the Lipschitz metric
- Generalizations to infinite-volume and higher-dimensional hyperbolic manifolds
- Generalizations to surfaces of infinite type

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*

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