Geometry and Topology Seminar

Series: Geometry and Topology Seminar Series

Coarse and fine geometry of the Thurston metric

David Dumas, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago,

I will present results of a recent collaboration with Anna Lenzhen, Kasra Rafi, and Jing Tao in which we study the geometry of Thurston's metric on Teichmueller space. This asymmetric metric is based on the Lipschitz constants of maps between hyperbolic surfaces. We study the coarse properties of Thurston metric geodesics in general, and some finer properties (local isometric rigidity, quantitative non-uniqueness of geodesics) in the case of the punctured torus.

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