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Delve into the advanced mathematical concepts of vertical Vafa-Witten invariants in this seminar on Algebraic Geometry. Explore how nested Hilbert schemes are utilized to express these invariants for a surface S in terms of universal power series. Learn about the reduction to toric surfaces and the explicit computation of generating functions through localization techniques. Examine the resulting formulas and gain insights into the intersection numbers on Hilbert schemes of points. Prepare for future discussions on applying Mochizuki's formula to horizontal Vafa-Witten invariants. Presented by Lothar Goettsche from ICTP, this lecture builds upon previous knowledge and sets the stage for further exploration in the field.
