In the 90s, Sullivan introduced the idea of studying families of dynamical systems with hyperbolic properties as Teichmüller spaces of 2-dimensional foliations or laminations. In these lectures, we will develop this idea in the case of the family of reparametrizations of the geodesic flow of a hyperbolic surface, providing a framework in which we hope to understand better the geometry of higher Teichmüller spaces (such as Hitchin components).

In the first lecture, we introduce the space of reparametrizations of the geodesic flow of a hyperbolic surface and describe its natural geometry. Speaker(s): Nicolas Tholozan (ENS)