Happening @ Michigan https://events.umich.edu/group/4889/rss RSS Feed for Happening @ Michigan Events at the University of Michigan. Dissertation Defense: Dynamics on the Moduli Space of Non-Orientable Surfaces (April 2, 2024 10:00am) https://events.umich.edu/event/120440 120440-21844767@events.umich.edu Event Begins: Tuesday, April 2, 2024 10:00am
Location: East Hall
Organized By: Dissertation Defense - Department of Mathematics

Abstract:
The moduli spaces of non-orientable hyperbolic surfaces have conjectural similarities to infinite volume geometrically finite hyperbolic manifolds. This thesis establishes some of the conjectured analogies to geometrically finite hyperbolic manifolds, which are useful in the context of understanding the geodesic flow on the unit cotangent bundle of the moduli space. In particular, it is shown that the Patterson-Sullivan measure is supported on the set of projective measured foliations containing no one-sided leaves. We then also show that the action of the mapping class group on the Teichmüller space, restricted to a finite covolume subset, is statistically convex-cocompact. We deduce from this that the Patterson-Sullivan measure is non-atomic, and the Bowen-Margulis measure on the unit cotangent bundle is finite, and the geodesic flow is mixing with respect to this measure.

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Presentation Wed, 20 Mar 2024 12:20:28 -0400 2024-04-02T10:00:00-04:00 2024-04-02T11:30:00-04:00 East Hall Dissertation Defense - Department of Mathematics Presentation East Hall