Speaker: Yufeng Jiang (University of Kansas)
Title:Vafa-Witten invariants via surface Deligne-Mumford stacks
Abstract: Motivated by S-duality conjecture, Tanaka-Thomas have developed a theory of Vafa-Witten invariants for projective surfaces. The invariants are defined by virtual localization on the moduli space of stable Higgs sheaves on a projective surface S. A Higgs sheaf is a pair (E, \phi) consisting of a torsion free coherent sheaf E, and a K_S-valued section of \phi E called the Higgs field. The extra data of the Higgs field provided information of sheaves on the Calabi-Yau threefold K_S, and the Vafa-Witten invariants of S receives contributions from the Calabi-Yau threefold. This is similar to Donaldson-Thomas invariants. In this talk I will talk about to define Vafa-Witten invariants for projective orbifold surfaces, and how the information of orbifold surfaces may give a chance to reduce the S-duality conjecture to the Langlands duality for projective curves.