Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices

Explore a lecture on Higgs bundles, convex cocompact subgroups of SU(1,n), and Slodowy slices presented by Brian Collier from the University of California. Delve into the challenges of determining the holonomy group of a local system associated with stable Higgs bundles. Discover how certain SU(1,n) Higgs bundles on compact Riemann surfaces define convex cocompact subgroups of SU(1,n), serving as holonomies of complex variations of Hodge structure. Learn about a method that produces representations in every component of the SU(1,n) character variety and how the structure of Higgs bundles describes associated complex hyperbolic manifolds as fibrations over surfaces. Examine the significance of Filip's recent work on SO(2,3)-Higgs bundles with Anosov holonomy representations in this context. This one-hour and eight-minute talk, presented at the University of Miami, is based on joint work with Zach Virgilio.