Junliang Shen: Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture

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Abstract: In this talk, I will discuss some structural results for the cohomology of the moduli of semi-stable SL_n Higgs bundles on a curve. One consequence is a new proof of the Hausel-Thaddeus conjecture proven previously by Groechenig-Wyss-Ziegler via p-adic integration. If time permits, we will also discuss the case where the rank of the Higgs bundle is not coprime to the degree, so that the moduli spaces are singular due to the presence of the strictly semi-stable loci. We will explain how intersection cohomology comes into play naturally. Based on joint work with Davesh Maulik.