Title：Arithmetic Simpson correspondence 

Speaker：Kang Zuo （University of Mainz and USTC）

Time：2018年9月28日（周五）    下午 14:00-15:30

Room：东区管理科研楼   0029cc金沙贵宾会1418室

Abstract：We propose an arithmetic Simpson correspondence for Higgs bundles over arithmetic schemes. It predicts that the monodromy of the Yang-Mills-Higgs connection on a rank-2 graded stable Higgs bundle on the projective line of degree -1 and with logarithmic singularities at four punctured points lies in an algebraic number ring if and only if the zero of the Higgs field is the image of a torsion point on the elliptic curve as double cover of the projective line ramified at those four points. We did construct 26 pieces complete solutions for monodromies lying in the integer ring and Higgs fields having zeros of order 1, 2, 3, 4 and 6. This is a joint project with J. Lu, X. Lu, R.R. Sun and J. B. Yang.