Geometric finiteness and Veech group extensions of surfaces groups

Spencer Dowdall (Vanderbilt University)

Monday 23rd November, 2020 16:00-17:00 Online


The notion of "convex cocompactness" and its generalization "geometric finiteness" play an important role the classical theory of Kleinian groups, that is, discrete subgroups of isometries of hyperbolic space. By means of analogy, in 2002 Farb and Mosher defined a subgroup of the mapping class group of a closed surface to be convex cocompact if it acts cocompactly on a quasi-convex subset of Teichmüller space. These subgroups have received much attention and it is known that they are precisely the subgroups whose corresponding surface group extensions are Gromov hyperbolic. However, it remains unclear precisely how geometric finiteness should manifest in mapping class groups nor how it should relate to the geometry of surface group extensions. This talk will look at perhaps the most compelling candidates for geometric finiteness in mapping class groups, namely Veech subgroups. I will explain the structure of Veech groups and show that their corresponding surface group extensions exhibit strong aspects of negative curvature and in fact are hierarchically hyperbolic. Joint work with Matt Durham, Chris Leininger, and Alex Sisto.

The talk will be preceded by a 30 minute tea time. The Zoom link for the seminar is and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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