报告题目：Analysis and Operator Theory on Bounded Symmetric Domains

报告人：Harald Upmeier (University of Marburg, Germany)

报告时间：2023.10.31，14:30-15:30

报告地点：金融数学实验室

报告摘要：In the previous lecture we described the geometry of bounded symmetric domains D of arbitrary rank r. The main concepts were the holomorphic transformation group G of the domain and the structure of the boundary ∂D. In this lecture we pass to the important idea of quantization. This means that one has to construct Hilbert spaces of holomorphic functions on D and operators acting on these Hilbert spaces. Starting with the familiar example of the unit disk, we introduce the Bergman spaces and Toeplitz operators acting on these Hilbert spaces. The deepest result in this direction is that the algebra T(D) generated by such Toeplitz operators (more precisely, the C* -algebra) has all its representations induced by the boundary components of D as described in the last lecture. In this sense the Toeplitz C*-algebra is a non-commutative model of the underlying bounded symmetric domain.

报告人简介：

Harald Upmeier，德国Marburg 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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