Moduli Spaces of Sheaves and Vafa-Witten Formula in Algebraic Geometry

Explore a comprehensive seminar on Algebraic Geometry focusing on moduli spaces of sheaves and the Vafa-Witten formula. Delve into the Hilbert scheme of points on a surface, learn about moduli spaces of stable sheaves, and examine the Vafa-Witten formula for Euler numbers of rank 2 sheaf moduli spaces. Investigate perfect obstruction theories and the virtual fundamental class, understanding their role in defining virtual versions of enumerative invariants. Consider the conjecture that the Vafa-Witten formula computes the virtual Euler number. Gain insights from speaker Lothar GOETTSCHE of ICTP as he builds upon a previous overview lecture to provide a detailed exploration of these advanced mathematical concepts.