报告题目:  Twisted Vafa-Witten invariants and S-duality

报告人： Prof. Yunfeng Jiang(University of Kansas, USA)

报告时间： 2019年12月6日（星期五）16:00-17:00

报告地点： 数学楼410

摘要:  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.

报告人简介：蒋云峰教授2007年毕业于加拿大英属哥伦比亚大学，获博士学位，之后在美国尤他大学和英国帝国理工学院从事博士后研究，现就职于美国堪萨斯大学数学系，主要从事代数几何和数学物理研究，在Journal Reine Angew Math.,  Advances in Math., Journal of Differential Geometry,  Internat.. Math. Res. Notices,  Pure and Applied Mathematics,  Mathematische Zeitschrift 等一流刊物上发表论文近40篇。欢迎有意向学习代数几何方向的本科生与研究生参加。