Jan Swoboda

Ends of the moduli space of Higgs bundles

We associate to each stable Higgs pair (A(0), Phi(0)) on a compact Riemann surface X a singular limiting configuration (A(infinity), Phi(infinity)), assuming that det Phi has only simple zeroes. We then prove. a desingularization theorem by constructing a family of solutions (A(t), t Phi(t) to Hitchins equations, which converge to this limiting configuration as t -> infinity. This provides a new proof via gluing methods, for elements in the ends of the Higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space.

Limiting configurations for solutions of Hitchin’s equation

We review recent work on the compactification of the moduli space of Hitchins self-duality equation. We study the degeneration behavior near the ends of this moduli space in a set of generic directions by showing how limiting configurations can be desingularized. Following ideas of Hitchin, we can relate the top boundary stratum of this space of limiting configurations to a Prym variety. A key r\^ole is played by the family of rotationally symmetric solutions to the self-duality equation on

Coisotropic displacement and small subsets of a symplectic manifold

\mathbb C

Asymptotics of the Weil-Petersson Metric

, which we discuss in detail here.