Title: Pressure Metrics for Deformation Spaces of Quasifuchsian Groups with Parabolics
Speaker: Lien-Yung "Nyima" Kao - George Washington University
Abstract: Thurston pointed out that one can use variations of lengths of closed geodesics on hyperbolic surfaces to construct a Riemannian metric on the Teichm\"uller space. When the surface is closed, Wolpert showed that Thurston's construction recovers the Weil-Petersson metric. Using thermodynamic formalism, McMullen proposed a new perspective to this Riemannian metric, and called it the pressure metric. In this talk, I will discuss how to extend this dynamical construction to spaces of quasiconformal deformations of (non-compact) finite area hyperbolic surfaces. This is a joint work with Harry Bray and Dick Canary.