报告题目：The Geometry of Bounded Symmetric Domains

报 告 人：Harald Upmeier (University of Marburg, Germany)

报告时间：2023.10.27，10:30-11:30

报告地点：金融数学实验室

报告摘要：Bounded symmetric domains are higher-dimensional generalizations of the unit disk in the complex plane. We investigate carefully the geometric properties of the unit disk and the unit ball, before discussing the bounded symmetric domains in general. The main topics are

• The group of holomorphic transformations (Moebius transformations) and the hyperbolic geometry

• The structure of the boundary and the behavior of geodesic curves at infinity

• Dynamical systems of holomorphic mappings

• Solution equations (completely integrable systems) on compact hermitian symmetric spaces

• Moduli spaces of Riemann surfaces

报告人简介：

Harald Upmeier，德国Marburge University数学与信息学院教授。Upmeier教授主要研究有界对称域上的Toeplitz算子理论，解析Hilbert模理论以及指标理论等，并做出了许多具有重要国际影响力的研究成果。这些研究工作横跨解析函数空间理论，代数几何，微分几何，李群的表示理论和数学物理等众多领域。其部分研究成果发表在Ann. of Math.，Adv. Math.，J. Reine Angew. Math.，Math. Ann.，Trans. Amer. Math.Soc.，J. Funct. Analysis，Int. Math. Res. Notices等国际一流数学刊物上。

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