Monday, October 29, 2018 at 4:30pm to 5:30pm
Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089
Francis Bonahon, USC
In her famous doctoral work, Maryam Mirzakhani studied the asymptotics of the lengths of multicurves in a hyperbolic surface X. These asymptotics are controlled by two constants. The first one depends only on the topological type of the surface and of the multicurves considered. The second constant µ(X) depends on the hyperbolic metric of X, and is defined as the Thurston volume of the set of measured geodesic laminations of length at most 1. I will discuss properties of µ(X) as a function on the moduli space of hyperbolic metrics on a given surface. The emphasis will be on the case of the one-punctured torus, as well as on experimental data and pretty pictures. This is joint work with Sabrina Enriquez, then an undergraduate at USC.