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Explore the intricacies of Vafa-Witten invariants in this advanced algebraic geometry seminar. Delve into the components of the fixpoint locus on the Vafa-Witten moduli space and examine the Vafa-Witten generating function's decomposition. Investigate the horizontal component, corresponding to stable sheaves, and the vertical component. Learn how the horizontal component contributes to VW invariants through the virtual Euler number of the moduli space of sheaves. Discover the Vafa-Witten predictions for generating function modularity and Laaracker's structure theorem for vertical Vafa-Witten invariants. Conclude by considering a conjectured analogue of Laaracker's theorem for horizontal invariants in this hour-long lecture by Lothar Goettsche from ICTP.
