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Higgs bundles on Riemann surfaces, I

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Alessandro Giacchetto
Mit, 15/01/2020 - 16:15 - 17:45
MPIM Seminar Room

The relation between representations of the fundamental group of a Riemann surface into the unitary group, flat connections on Hermitian vector bundles, and stable holomorphic bundles on the surface, goes back to the celebrated theorem of Narasimhan and Seshadri. The case of representations into a non-compact reductive Lie group required the introduction of new holomorphic objects on the Riemann surface, called Higgs bundles. In this first session, we will introduce the moduli spaces of representations, connections and Higgs bundles in the case of SL(r,C), and we will move the first steps towards a proof of the celebrated non-abelian Hodge correspondence.


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