Representations of surface groups and Higgs bundles - II

1 hour 2 mins 38 secs, 866.48 MB, MPEG-4 Video 480x360, 25.0 fps, 44100 Hz, 1.84 Mbits/sec

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Description:	Gothen, P (Universidade do Porto) Monday 10 January 2011, 11:30-12:30

Created:

2011-01-13 09:36

Collection:

Moduli Spaces

Publisher:

Isaac Newton Institute

Gothen, P

Language:

eng (English)

Credits:

Author:	Gothen, P
Producer:	Tim Cooper


Abstract:	A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic bundle and a holomorphic one-form, the Higgs field, with values in a certain associated vector bundle. A theorem of Hitchin and Simpson says that a stable Higgs bundle admits a metric satisfying Hitchin's equations. Together with the Theorem of Corlette and Donaldson, the Hitchin-Kobayashi correspondence generalizes the classical Hodge decomposition of the first cohomology of the Riemann surface, providing a correspondence between isomorphism classes of Higgs bundles and representations of the fundamental group of the surface.

Abstract:

A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic bundle and a holomorphic one-form, the Higgs field, with values in a certain associated vector bundle. A theorem of Hitchin and Simpson says that a stable Higgs bundle admits a metric satisfying Hitchin's equations. Together with the Theorem of Corlette and Donaldson, the Hitchin-Kobayashi correspondence generalizes the classical Hodge decomposition of the first cohomology of the Riemann surface, providing a correspondence between isomorphism classes of Higgs bundles and representations of the fundamental group of the surface.

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