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Explore advanced concepts in algebraic geometry through this ICTP/IGAP seminar focusing on refined invariants and Vafa-Witten invariants. Delve into the application of perfect obstruction theories and virtual invariants to define virtual Euler numbers of moduli spaces of sheaves and their refinement by the virtual chi_y-genus. Examine the moduli space of Higgs pairs and its role in defining Vafa-Witten invariants. Review localization and virtual localization with respect to C*-actions. Cover topics such as modular spaces, virtual dimensions, subsheats, model spaces, and tangent solutions. Gain insights from speaker Lothar GOETTSCHE of ICTP in this comprehensive 1-hour 7-minute lecture, building upon previous discussions on moduli spaces of sheaves on surfaces.
