Geometry & Physics Seminar

Motivated by the S-duality conjecture, Tanaka-Thomas have defined the Vafa-Witten invariants for projective surfaces by constructing a perfect obstruction theory on the moduli space of stable Higgs sheaves on a smooth surface. They proved that the generating function of the invariants satisfies modularity properties. The study of the Higgs sheaves on a surface implies that there exists threefold contributions to the Vafa-Witten invariants. In this talk I will talk about the Vafa-Witten invariants via surface Deligne-Mumford stacks. There are many interesting surface Deligne-Mumford stacks which are pretty useful in mirror symmetry. We will define the Vafa-Witten invariants for surface Deligne-Mumford stacks and calculate some examples.

In the second part of the talk, I will explain one special case of root stacks, and how the Vafa-Witten invariants are related to the geometric Eisenstein series over functional field of curves.
Speaker(s): Yunfeng Jiang (University of Kansas)