Geometry MMA Seminar: The Boundary at Infinity and Geodesic Currents

Speaker: Noelle Sawyer, Southwestern University

Title:   The Boundary at Infinity and Geodesic Currents

Abstract:  I plan to spend the first half talking about the boundary at infinity, geodesic currents (a measure on the space of geodesics), and why they're both interesting tools to help to understand geometric notions. In the second half, I will go more in depth about how I use these tools: Given a surface, the marked length spectrum (MLS) is the collection of the lengths of the closed geodesics, with each length marked by the free homotopy class it belongs to. Under certain conditions, information on most of the MLS is enough to completely determine the metric of the surface; I will give some intuition on how and why geodesic currents tie into the proof.

Time: Monday, November 14, 2022 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208