9-13 April 2018
Organisers: Mladen Bestvina, Tara Brendle, Chris Leininger
The mapping class group and Teichmüller space tie together numerous fields of mathematics, and are related in many ways to the topics featured in the rest of the Symposium. This workshop will focus on geometric aspects of the mapping class group and of Teichmüller space equipped with a standard metric, such as the Teichmüller or Weil-Petersson metric. It will place special emphasis on the coarse, or large-scale, geometry of these spaces, as well as the coarse geometry of various associated complexes such as Harvey's curve complex.
Recently great strides have been made in this direction, for example quasi-isometric rigidity has been established for mapping class groups and Teichmüller spaces. Efforts have now shifted to problems such as the Ending Lamination Conjecture for the Weil-Petersson metric and existence and classification problems for convex cocompact subgroups of mapping class groups.
It is precisely the connections with other fields, especially those emphasised in this Symposium, that feed into and benefit from research in mapping class groups and Teichmüller space. For example, the invaluable curve complex tools, such as the subsurface projections and hierarchies due to Masur and Minsky, were developed to resolve the Ending Lamination Theorem for hyperbolic 3-manifolds (the motivation for the conjecture of the same name mentioned above). Convex cocompactness on the other hand is intimately related to the geometry of surface bundles. In addition, there has been considerable technology from mapping class groups to the study of automorphism groups of free groups, which will be the topic of the subsequent week's workshop.
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Mathematics Research Centre
University of Warwick
Coventry CV4 7AL - UK