# Seminars & Colloquia Calendar

Geometric Analysis Seminar

## Construction of the moduli space of Higgs bundles using analytic methods.

#### Yue Fan, University of Maryland

Location:  via Zoom, https://rutgers.zoom.us/j/93880280324
Date & time: Tuesday, 27 October 2020 at 2:50PM - 3:50PM

Abstract: Introduced by Hitchin, a Higgs bundle $$(E,\Phi)$$ on a complex manifold $$X$$ is a holomorphic vector bundle $$E$$ together with an $$\End E$$-valued holomorphic 1-form $$\Phi$$. The moduli space of Higgs bundles was constructed by Nitsure where $$X$$ is a smooth projective curve and by Simpson where $$X$$ is a smooth projective variety. They both used Geometric Invariant Theory, and the moduli space is a quasi-projective variety. It is a folklore theorem that the Kuranishi slice method can be used to construct this moduli space as a complex space where $$X$$ is a closed Riemann surface. I will present a proof of this folklore theorem and show that the resulting complex space is biholomorphic to the one in the category of schemes. Moreover, I will briefly talk about some applications of this new construction.