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Representations of surface groups and Higgs bundles - II

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Moduli Spaces

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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