Jan Swoboda: The large scale geometry of the Higgs bundle moduli space
Abstract: In this talk I will explain recent joint work with Rafe Mazzeo, Hartmut Weiss and Frederik Witt on the asymptotics of the natural L2-metric GL2 on the moduli space M of rank-2 Higgs bundles over a Riemann surface Σ as given by the set of solutions to the so-called self-duality equations
{0=∂¯AΦ0=FA+[Φ∧Φ∗]
for a unitary connection A and a Higgs field Φ on Σ. I will show that on the regular part of the Hitchin fibration (A, Φ) → det Φ this metric is well-approximated by the semiflat metric Gsf coming from the completely integrable system on M. This also reveals the asymptotically conic structure of GL2, with (generic) fibres of the above fibration being asymptotically flat tori. This result confirms some aspects of a more general conjectural picture made by Gaiotto, Moore and Neitzke. Its proof is based on a detailed understanding of the ends structure of M. The analytic methods used there in addition yield a complete asymptotic expansion of the difference GL2−Gsf between the two metrics.
Recording during the meeting "Gauge Theory and Complex Geometry" the June 20, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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{0=∂¯AΦ0=FA+[Φ∧Φ∗]
for a unitary connection A and a Higgs field Φ on Σ. I will show that on the regular part of the Hitchin fibration (A, Φ) → det Φ this metric is well-approximated by the semiflat metric Gsf coming from the completely integrable system on M. This also reveals the asymptotically conic structure of GL2, with (generic) fibres of the above fibration being asymptotically flat tori. This result confirms some aspects of a more general conjectural picture made by Gaiotto, Moore and Neitzke. Its proof is based on a detailed understanding of the ends structure of M. The analytic methods used there in addition yield a complete asymptotic expansion of the difference GL2−Gsf between the two metrics.
Recording during the meeting "Gauge Theory and Complex Geometry" the June 20, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities:
- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area
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