Title: Bers’ simultaneous uniformization theorem and the intersection of Poincaré holonomy varieties
Speaker: Shinpei Baba (Osaka University)
Date: 09 November 2022
Time: 4:00 pm
Venue: LH-1 (In person)
The Poincaré holonomy variety (or $sl(2, C)$-oper) is the set of holonomy representations of all complex projective structures on a Riemann surface. It is a complex analytic subvariety of the $PSL(2, C)$ character variety of the underlying topological surface. In this talk, we consider the intersection
of such subvarieties for different Riemann surface structures, and we prove the discreteness of such an intersection. As a corollary, we reprove Bers’
simultaneous uniformization theorem, without any quasiconformal deformation theory.