数学研究所
数学科学全国重点实验室

学术报告

偏微分方程研讨班

Speaker: 郭庭榕 教授 (台湾师范大学)

Inviter: 邱国寰

Language:        English

Title: Spherical metric with integer conical singularities on flat tori

Time&Venue: 2025年7月13日（星期日）9:30-10:30

&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.