About
I maintain active research programs in the study ofhyperbolic 3-manifolds and in Higher Teichm uller theory. In hyperbolic 3-manifolds, my recentwork, in collaboration with Je Brock, Ken Bromberg, Cyril Lecuire and Yair Minsky, has focussedon harnessing the techniques developed in the solution of Thurston's Ending Laminationto further our understanding of deformation spaces of hyperbolic 3-manifolds. For example,we have developed criteria to characterize when a sequence of Kleinian groups has a convergentsubsequence and have established a powerful generalization of Thurston's Bounded Image Theorem.In Higher Teichmuller theory, in collaboration with Martin Bridgeman, Francois Labourieand Andres Sambarino, I use techniques from the thermodynamic formalism to study deformationspaces of Anosov representations. In particular, we constructed an analytic mappingclass group invariant Riemannian metric on the Hitchin component which is an analogue of theclassical Weil-Petersson metric on Teichm uller space. In collaboration with Kostas Tsouvalas, Ihave studied topological restrictions on groups which admit Anosov representations.
