报告时间：2026年6月15日 上午10:00开始

报 告 人：郭庭榕（教授，台湾师范大学数学系）

报告地点：9-102

报告题目：Global and finer geometry of generalized Lame equation

报告摘要：The Generalized Lamé Equation (GLE) plays a central role in the theory of integrable systems, including the KdV hierarchy and finite-gap integration theory. Recently, a comprehensive global theory of the GLE has been developed by Chou, Wang, and Wu. A key achievement of their work is the explicit determination of the total degree of the addition map, which governs the global geometry of the GLE. As a consequence, both the monodromy problem and the isomonodromic deformation problem can be effectively characterized through an associated pre-modular form.

Beyond its global geometry, the GLE admits a finer geometric structure from the perspective of monodromy. This refined geometry reveals richer features of the equation and, in particular, provides a framework for understanding and controlling the trajectories of isomonodromic deformations.

In this talk, I will first review the theory developed by Chou, Wang, and Wu, and then introduce this finer geometric structure of the GLE. This is a joint work with Xuanpu Liang.

报告人简介：郭庭榕，台湾师范大学教授。2011年毕业于台湾清华大学，2011-2016年于台大数学科学中心任博士后研究，2016-现今于台湾师范大学担任助理教授，副教授，教授。并于2025年获得台湾师范大学特聘教授荣誉。主要研究工作方向为椭圆曲线上非线性曲率方程(singular Liouville equation)的爆破解研究，拉梅方程的单值化问题及酉值问题之研究，相关工作皆发表在JMPA, Math. Ann, JDG,CAG 等国际顶尖期刊。