Speaker: 郭庭榕教授，台湾师范大学

Inviter: 邱国寰

Title: Spherical metric with integer conical singularities on flat tori

Language: English

Time & Venue: 2025.07.13 09:30-10:30 思源楼S813

Abstract: In this talk, I will introduce the problem of finding a spherical metric on a flat torus with prescribed integer conical singularities. For such metrics with integer cone angles, the method of topological degree theory completely fails. Instead of using degree theory from PDE, we apply the integrability of the curvature equation, which allows us to translate the problem into the study of the monodromy representation of an associated elliptic Fuchsian ODE. A criterion for the existence of such a metric will be presented using the language of monodromy representations. The following topics will be covered in this talk:

1. Motivation from conformal geometry.

2. From PDE to ODE via integrability.

Survey on known results in the literature.