Vortrag: "The asymptotic geometry of the Hitchin metric"

Abstract:

The moduli space of Higgs bundles on a Riemann surface carries a distinguished hyperkähler metric, the so-called Hitchin metric. By virtue of being the total space of an integrable system, its regular part carries a simpler, semi-flat metric. In recent joint work with Rafe Mazzeo, Jan Swoboda and Frederik Witt we show that in the ends of this moduli space the Hitchin metric is well-approximated by the semi-flat metric. This is based on our earlier construction of solutions to Hitchin’s equation with large Higgs fields. In my talk I will spend most of the time explaining the basics of Higgs bundle theory, leading up to the construction of these two different metrics.