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Geometric and analytic aspects of Higgs bundle moduli spaces (GGT-Seminar)

Geometric and analytic aspects of Higgs bundle moduli spaces (GGT-Seminar)
Date:

19.01.2016

Place:

SR 1.067 (20.30) 

Speaker:

Dr. Jan Swoboda

Time:

16:00 Uhr

Abstract: 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 Mk,d of stable Higgs bundles (of rank k and degree d) on a compact Riemann surface āˆ‘. I shall in particular discuss the construction of Mk,d as the space of gauge equivalence classes of solutions to Hitchinā€™s selfduality equations. Some recent results (obtained jointly with Rafe Mazzeo, Hartmut Weiß and Frederik Witt) concerning the structure of ends of M2,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 M2,d with its counterpart comprising singular solutions on a noded Riemann surface.