Lipschitz metric on Teichmueller space
October 22 to October 26, 2012
American Institute of Mathematics,
Palo Alto, California
and Jing Tao
This workshop will be devoted to recent developments and new directions in Teichm�ller 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 Originally introduced by Thurston in an unpublished manuscript in 1986, the Lipschitz metric is an "asymmetric metric" on Teichm�ller space.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 Teichm�ller 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 Teichm�ller 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
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.