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Presence
ICTP Leonardo Da Vinci Building - Budinich Lecture Hall (only if provided with a green pass)

Abstract: In the last lecture we introduced moduli spaces of sheaves on surface and then defined perfect obstruction theories and virtual invariants. We start this lecture by applying this to define the virtual Euler numbers of moduli spaces of sheaves, and their refinement by the virtual chi_y-genus. We will then introduce the moduli space of Higgs pairs and use it to define Vafa-Witten invariants. This also requires a review of localization and virtual localization with respect to $C^*$-actions.