Groups and Dynamics

We will present a pair of flexible and highly degenerate constructions of objects related to Thurston’s Lipschitz metric on Teichmüller space. In particular, we will explain how to construct irregular geodesics for Thurston’s metric on Teichmüller space and how to construct sums of Fuchsian representations of surface groups whose limit cones are polyhedra. Both constructions are “as degenerate as possible” in appropriate senses. We will emphasize the close relationship of these constructions with a counterintuitive theorem of Thurston on the generic simplicity and stability of solutions to a length-ratio optimization problem on hyperbolic surfaces