深谷賢治 , 杨琳 , 塞巴斯蒂安·赫勒 , 河井公大朗

Shinpei Baba

2025年05月20日 14:45 至 16:30

A3-4-301

Zoom 815 762 8413 (BIMSA)

In this talk, we discuss the intersection of certain analytic Lagrangians in the $PSL(2, C)$-character variety of a closed surface. A holomorphic quadratic differential on a closed Riemann surface corresponds to a complex projective structure. In addition, holomorphic quadratic differentials on a fixed Riemann surface form a complex affine vector space. Then, by the holonomy map of complex projective structures, this vector space properly maps onto a smooth analytic Lagrangian subvariety of the space of representations of the surface group into $PSL(2, C)$. In this talk, given two (marked) closed Riemann surface structures of the same topological type, we show that their corresponding subvarieties intersect in an infinite discrete set.