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Fakultät für Mathematik

Karlsruher Institut für Technologie
D-76128 Karlsruhe
Tel.: +49 721 608-43800

Geometric and analytic aspects of Higgs bundle moduli spaces

Referent: Dr. Jan Swoboda
Ort: SR 1.067 (20.30)
Termin: 19.1.2016, 16:00 - 17:00 Uhr
Gastgeber: PD Dr. Manuel Amann


In this talk, I aim to give an overview of some known results and several open questions concerning geometric and topological properties of the moduli space \mathcal{M}_{k,d} of stable Higgs bundles (of rank k and degree d) on a compact Riemann surface \Sigma. I shall in particular discuss the construction of \mathcal{M}_{k,d} as the space of gauge equivalence classes of solutions to Hitchin’s selfduality equations. Some recent results (obtained jointly with Rafe Mazzeo, Hartmut Weiß and Frederik Witt) concerning the structure of ends of \mathcal{M}_{2,d} as well as the large scale geometry of a naturally defined hyperkähler metric will be presented. If time permits, I will also discuss a gluing construction which allows to compare \mathcal{M}_{2,d} with its counterpart comprising singular solutions on a noded Riemann surface.

Ab 15:30 Uhr findet in Raum 1.062 im Kollegiengebäude Mathematik (Geb. 20.30) ein gemeinsamer Tee statt. Herzliche Einladung!