Student Dynamics/Geometry Topology Seminar

It's a theorem of Otal that the marked length spectrum is a complete isometry invariant for closed surfaces of negative sectional curvature. The same can't be said for the unmarked length spectrum -- Sunada's construction provides examples of surfaces which are length isospectral but not isometric. Generalizing the methods of Maungchang, we'll discuss an ongoing attempt to salvage the unmarked length spectrum as an isometry invariant. In the process, we'll take a tour through some touchstone ideas in surface topology, including the coarse geometry of the curve complex and the Teichmüller space.

Recommended background for surface-level understanding: basic exposure to the fundamental group, covering spaces, and the classification of surfaces. For mid-level understanding: some exposure to Riemannian and/or hyperbolic geometry, the curve complex, and Teichmüller space. For technical understanding: some exposure to coarse geometry, the Gromov boundary of the curve complex and the Thurston boundary of the Teichmüller space.

Speaker(s): Max Lahn (University of Michigan)