Groups and Dynamics Seminar

Classical Teichmuller theory bridges geometry, analysis, and dynamics through the study of surface group representations into rank-one Lie groups. In recent years, interest has gravitated towards understanding deformation spaces of discrete and faithful representations into higher-rank Lie groups — a field known as higher Teichmuller-Thurston theory. A central object in this setting is the Hitchin component, which serves as a well-behaved higher-rank analogue of Teichmuller space. In this talk, I will outline how tools from dynamics — including geodesic flows, reparameterizations, and thermodynamic formalism — can be leveraged to generalize the Weil-Petersson metric from the classical setting to Hitchin components. I will conclude by highlighting some recent results and suggesting directions for future research. This is a candidacy talk.