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Seminar by Jan Swoboda (LMU München)

Title: The large scale geometry of the moduli space of Higgs bundles

2017.05.10 | Christine Dilling

Date Wed 10 May
Time 14:15 15:15
Location 1531-211 Kol-D

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.