走向现代数学学术报告 - 潘会平副教授（No. 809)

报告题目：Ray structures on Teichmuller space

报 告 人： 潘会平 副教授（华南理工大学）

邀 请 人：鲍官龙副教授、朱剑峰教授

报告时间：2025年9月8日 10:00

报告地点：东海岸校区-D209

报告摘要：Given an oriented closed surface S of genus at least two, the Teichmuller space of S is the space of equivalence classes of complex structures on S. It is also the space of equivalence classes of hyperbolic structures on S. Deformations of these structures provide several types of ray structures on the Teichmuller space. In this talk, we will show a transition between Teichmuller geodesics and Thurston geodesics via harmonic map (dual) rays. As applications, (1) we construct a new family of Thurston geodesics, the harmonic stretch lines, and show the existence and uniqueness of such lines for any two hyperbolic surfaces in the Teichmuller space; (2) we show that the envelope of the Thurston metric is a cone over a cover and depends continuously on the endpoints. This is based on joint works with Michael Wolf (arXiv:2206.01371 and arXiv:2401.06607).

报告人简介：潘会平，华南理工大学数学学院副教授，研究方向为复分析（Teichmuller理论），主 要研究曲面上的复结构、双曲结构、平坦结构等几何结构，以及这些结构之间的形变，相 关论文在Acta Math.、 Math. Ann.、Trans. Amer. Math. Soc.、Int. Math. Res. Not. IMRN、Sci. China Math.等期刊发表或接受发表。

数学研究所

2025年9月2日