Motivic local systems and motivic Higgs bundles

时间:2023年12月29日 9:00-11:15    


主讲人:左康 教授(武汉大学)

主持人:张通 教授


In this short course I shall explain the recent joint work with Jinbang Yang in detail. Introduction to non-abelian p-adic Hodge theory, Higgs de Rham flow, p-adic Simpson correspondence for periodic Higgs bundles, Deligne’s p to l companions, Yu’s work on numerical characteristic p Simpson correspondence, Drinfeld’s work on Langlands correspondence for rank two l-adic local systems with cusps, Grothendieck-Messing deformation theorem for log abelian schemes. As an application we construct all rank-2 motivic local systems over the complex projective line with 4 punctures with given type of local monodromy: unipotent around {0, 1, λ} and quasi unipotent around infinity with eigenvalues {-1, -1}. It is remarkable, recently Lam-Litt provided a totally different approach to the above by using Katz middle convolution.


左康教授博士毕业于德国Bonn大学,师从 Hirzebruch 教授。左康教授现任职于武汉大学,主要研究方向为代数几何。他在代数簇基本群的表示、模空间的双曲性、Coleman-Oort猜测、p进Simpson对应等多个方向上取得了一系列杰出的成果。