Simultaneous uniformization and algebraic correspondences

YMSC Topology Seminar

Organizers：

陈伟彦、高鸿灏、黄意、林剑锋、孙巍峰

Speaker：

Sabyasachi Mukherjee

Tata Institute of Fundamental Research

Time：

Mon.,16:00-17:00, Sept. 8, 2025

Venue：

C654, Shuangqing Complex Building A

Online：

Zoom ID: 405 416 0815

Password: 111111

Abstract:

Algebraic correspondences on the Riemann sphere provide a rich and interesting class of conformal dynamical systems that contains rational dynamics and Kleinian group actions as important sub-classes. We will discuss two combination theorems in the world of algebraic correspondences. The first one combines holomorphic Blaschke products with genus zero orbifolds, while the second combines/uniformizes two possibly non-homeomorphic genus zero orbifolds. The latter result can be regarded as an extension of the Bers' simultaneous uniformization theorem in the world of algebraic correspondences. Time permitting, we will also present new complex-analytic realizations of Teichmüller spaces of punctured spheres in parameter space of correspondences.