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学术报告:Moduli Space of Riemann Surfaces and Universal Teichmuller Space

发布时间:2017年09月13日 浏览次数:发布者:mathky

报告人:张丽萍教授

厦门大学马来西亚分校

报告题目:Moduli Space of Riemann Surfaces and Universal Teichmuller Space

报告时间: 2017年9月20日下午15:00

报告地点:海韵行政楼B313

内容摘要:The moduli space of a surface is the space of all different complex structures on the surface. The moduli space of a hyperbolic surface is a complex manifold equipped with a Kahler metric – the Weil-Petersson metric, which is induced by the natural inner product of quadratic differentials. In this talk, we discuss the Weil-Petersson geometry of the moduli spaces of hyperbolic surfaces with finite area, as well as the universal Teichmüller space (the universal moduli space). In particular, we discuss the construction of the potential of the Weil-Petersson metric– the classical Liouville action which was motivated by string theory. We demonstrate the relation between the Liouville action and the renormalized volume of a corresponding hyperbolic three manifold. We also discuss the local index theorem on the moduli spaces.

报告人简介张丽萍博士在2016年1月加入厦门大学马来西亚分校成为数学教授。她于2002年在美国纽约州立大学石溪分校 (State University of New York at Stony Brook) 取得数学博士学位,主要的研究领域是数学物理及复变函数论,也曾经研究过可积系统,随机过程及理论物理方面的课题。目前主要的研究兴趣是在解析数论及数学物理。

学院联系人:谭绍滨教授、余铌娜助理教授

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