Seminar Event Detail

Geometry & Physics

Date:  Monday, September 24, 2018
Location:  4096 East Hall (4:00 PM to 6:00 PM)

Title:  Vafa-Witten invariants for surface Deligne-Mumford stacks

Abstract:   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:  Yunfeng Jiang
Institution:  University of Kansas

Event Organizer:     


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