Asymptotics in Hitchin's Moduli Space
Explore the intricate structure of the rank 2 Higgs bundles moduli space in this 53-minute lecture by Richard Wentworth from the University of Maryland. Delve into the various notions of ideal points at infinity arising from different incarnations of the space via the nonabelian Hodge theorem. Examine the refinement of the Morgan-Shalen compactification of the Betti moduli space, the algebraic geometry of the C-star action on the moduli space, and the analytic "limiting configurations" of solutions to the Hitchin equations. Investigate how the nonabelian Hodge correspondence extends as a map between the latter two (partial) compactifications, and discover the surprising non-continuity of this extension. Gain insights into the connections between integrable systems, hyperkaehler reduction, mirror symmetry, and supersymmetric gauge theory within this rich mathematical framework.