报告题目: Hilbert Modules and Singular Vector Bundles on Bounded Symmetric Domains

报 告人: Prof. Harald Upmeier

单 位: Marburge University (German)

报告时间: 2022/11/08, 16:00-17:00

Zoom会议: 838-0573-4198

会议密码: 2022

摘 要:Bounded symmetric domains in several complex variables are of fundamental importance in differential geometry, representation theory of Lie groups, and the theory of Toeplitz operators. In the first part of the talk we describe the most important Hilbert modules on bounded symmetric domains: the weighted Bergman spaces of holomorphic functions and the Hardy space. The second part of the talk introduces Hilbert submodules related to algebraic subvarieties of the underlying domain. The main problem is to determine the so-called eigenbundle (a generalization of the Cowen-Douglas hermitian vector bundle) associated with the Hilbert submodule. It is shown that this eigenbundle is a holomorphic vector bundle with singularities along the subvarieties. The fibres and the rank of the vector bundle are explicitly computed.

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。其研究成果发表在Ann. of Math.，Adv. Math.，Trans. Amer. Math.，J. Funct. Analysis，Math. Ann.，Int. Math. Res. Notices等国际一流数学刊物上。

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