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Algebra Seminar: Twisted Vafa-Witten invariants and the S-duality conjecture

Speaker: Yunfeng Jiang, University of Kansas

Title:  Twisted Vafa-Witten invariants and the S-duality conjecture

Abstract:  For a real four manifold,  the S-duality conjecture of Vafa-Witten (1994) predicts that the S-transformation sends the gauge group SU(r)-invariants counting instantons to the Langlands dual gauge group SU(r)/Z_r-invariants; and both of the invariants satisfy modularity properties.  The SU(r)-Vafa-Witten invariants have been constructed by Tanaka-Thomas using the moduli space of semistable Higgs bundle or sheaves on a smooth projective surface. In this talk I will present the idea of using moduli space of  twisted sheaves and twisted Higgs sheaves on a projective surface  to define the  Langlands dual gauge group SU(r)/Z_r-Vafa-Witten invariants, and prove the S-duality conjecture of Vafa-Witten for projective plane in rank two and K3 surfaces in prime ranks.
 

Dial-In Information

https://ksu.zoom.us/j/350392106

Zoom Meeting ID 350 392 106

Monday, April 13 at 3:30pm to 4:30pm

Event Type

Lecture, Colloquia, Seminar

Topic

Research and Innovation

Audience

Current students, Faculty

Department
Mathematics, Department of, Homepage Calendar
Hashtag

#KSU-Algebra Seminar

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