Friday April 25th, 2025 | |
| Time: | 2:15 PM - 3:15 PM |
| Title: | Random Measured Laminations and Teichmüller Space |
| Speaker: | Tina Torkaman, University of Chicago |
| Abstract: | |
| In this talk, we introduce a canonical geodesic current $KX$ for each $X ∈ T_g$, 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 $X → KX$ 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. | |