Seminar

In his thesis, McShane described a remarkable identity concerning the lengths of simple closed geodesics on a once-punctured torus with a complete, finite-volume hyperbolic structure. He gave a geometric proof using ergodic theoretic results of Birman-Series. A few years later, Bowditch gave a more direct proof using Markoff triples. Finally, Mirzakhani vastly generalized it in the course of her work on the volumes of moduli spaces of hyperbolic surfaces. In this talk, I will outline McShane’s original argument and discuss the subsequent generalizations.