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The large scale geometry of the moduli space of Higgs bundles

Jan Swoboda
(LMU München)
Seminar
Wednesday, 10 May, 2017, at 14:15-15:15, in Koll. D (1531-211)
Abstract:

In this talk I will explain recent joint work with Rafe Mazzeo , Hartmut Wei{ \ss } and Frederik Witt on the asymptotics of the natural $L^2$ metric on the moduli space of rank- $2$ Higgs bundles over a Riemann surface $\Sigma$ . It will be shown that on the regular part of the Hitchin fibration this metric is well-approximated by the so-called semiflat metric coming from the algebraic completely integrable system moduli space is endowed with. This result confirms some aspects of a more detailed conjectural picture made by Gaiotto , Moore and Neitzke . In the second half of the talk, I will explain some of my current results concerning the behaviour of the moduli space when $\Sigma$ degenerates to a Riemann surface with nodes. These are based on a detailed understanding of the transition between smooth and singular geometric operators along this degeneration, and I will pay particular attention to these more analytic aspects of the theory.

Organised by: QGM
Contact person: Jørgen Ellegaard Andersen