高水平大学建设系列报告976号

数学科学学院学术报告[2024]096号

讲座题目：Ray structures on Teichmuller spaces

报 告 人： 潘会平（华南理工大学数学学院）

报告时间： 2024年10月16日 10：30—11：30

报告地点： 汇文楼1420

报告内容： Teichmuller space admits several ray structures, such as the Teichmuller geodesic ray, Thurston stretch ray, harmonic map (dual) ray, grafting ray, etc. In the first part of this talk, we will depict harmonic map ray structures on Teichmuller space as a geometric transition between Teichmuller ray structures and Thurston geodesic ray structures. In particular, by appropriately degenerating the source of a harmonic map between hyperbolic surfaces, the harmonic map rays through the target converge to a Thurston geodesic; by appropriately degenerating the target of the harmonic map, those harmonic map dual rays through the domain converge to a Teichmuller geodesic. In the second part, we will discuss applications to Thurston metric. While there may be many Thurston metric geodesics between a pair of ordered points in Teichmuller space, we select a unique Thurston geodesic through those points in a canonical way. This is a joint work with Michael Wolf (arXiv:2206.01371 and arXiv:2401.06607).

报告人简历： 潘会平，博士，华南理工大学数学学院副教授，研究方向为复分析与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，相关论文发表在Math. Ann.、Trans. Amer. Math. Soc.、Int. Math. Res. Not. IMRN、Sci. China Math. 等期刊。

欢迎师生参加！

邀请人：周泽                                                                  

数学科学学院/数学研究所

2024年10月9日