Moduli Spaces of Sheaves, Vafa-Witten Formula and Virtual Invariants

Explore an advanced seminar on Algebraic Geometry focusing on moduli spaces of sheaves, the Vafa-Witten formula, and virtual invariants. 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 in this comprehensive exploration of complex algebraic geometry concepts.