Yue Fan will speak on

Construction of the moduli space of Higgs bundles using analytic methods

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.