Schedule for 2026-2027

November 12th, 2026

Speaker: Federica Bessi (SISSA)

Title: The compactification of Teichmüller space via geodesic currents 

Abstract: What happens to a hyperbolic surface when the lengths of some of its curves tend to zero or become arbitrarily large? This question leads to the problem of compactifying Teichmüller space. In this talk, I will introduce an approach to this problem based on the theory of geodesic currents, developed by Francis Bonahon. The idea is to represent both closed curves and hyperbolic metrics on a given surface as measures on the space of geodesics of the hyperbolic plane. An intersection form on this space allows us to relate these different objects and, in particular, to recover the length of curves and their geometric intersection numbers. I will then show how this construction leads to a compactification of Teichmüller space, recovering the classical one introduced by Thurston.