Speaker: Yunfeng Jiang 蒋云峰 (ShanghaiTech University and University of Kansas)

Time: Friday, 15.Nov.2019, 1:30--2:30

Place: Room 402, Mathematical Building

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-homas 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.