Thurston's Asymmetric Metric on Teichmüller Space Revisited

Explore a recorded talk from the Big Ideas in Dynamics in Geometry: A Hybrid Conference, delivered by Jeffrey Danciger from UT Austin. Delve into the fascinating world of hyperbolic structures on surfaces with negative Euler characteristic and their organization within the classical Teichmüller space. Examine Thurston's asymmetric metric on Teichmüller space, which compares hyperbolic structures through their length spectra. Discover how this concept is generalized to d-tuples of hyperbolic structures and positive representations of fundamental groups into real split, semi-simple Lie groups of higher rank. Learn about the joint work with François Guéritaud and Fanny Kassel, which uncovers interesting geometric and dynamical invariants associated with these generalizations. Gain insights into this complex topic during this one-hour presentation, recorded on September 28th, 2024, at the University of Illinois Chicago.