Geometry, Topology and Dynamics Seminar
Tina Torkaman
University of Chicago
Random Measured Laminations and Teichmüller Space
Abstract: In this talk, we introduce a canonical geodesic current $KX$ for each $X\in T_g$, representing a randomly chosen simple closed geodesic on $X$. We establish results analogous to Bonahon's work on the Liouville measure. In particular, we show that the map $X\mapsto KX$ defines a proper embedding of Teichmüller space $T_g$ into the space of geodesic currents. This embedding leads to a compactification of $T_g$ that differs from Thurston's compactification (which Bonahon's results yield via the Liouville measure). We will discuss the construction of $KX$ and its geometric properties. This is joint work with Curt McMullen.
Wednesday November 12, 2025 at 3:00 PM in 636 SEO