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Title:
Cohomology of certain moduli spaces of sheaves
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Abstract:
Cohomology of the moduli space of vector bundles on a curve has been studied for decades. In this talk, I will discuss some closely related moduli spaces, including moduli of Higgs bundles on a curve and moduli of sheaves on a Fano surface. Considerations from non-abelian Hodge theory and modern enumerative geometry of Calabi-Yau 3-folds predict surprising structures for the cohomology of these classical moduli spaces. I will discuss these predictions and some recent progress, without assuming any previous knowledge of non-abelian Hodge theory or enumerative geometry.
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