Critical points, Riemann surface and multiplication operators defined by finite Blaschke products on the Bergman space -东北师范大学数学与统计学院

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Critical points, Riemann surface and multiplication operators defined by finite Blaschke products on the Bergman space

时间：2025年09月22日 15:55 点击数：

报告人：黄寒松

报告地点：腾讯会议ID：801-746-432

报告时间：2025年09月25日星期四15:30-16:30

邀请人：李春光、安庆楠

报告摘要：

For a finite Blaschke product $B$, the von Neumann algebra $\mathcal{V}^*(B) = \{M_B, M_B^*\}'$ has been thoroughly studied,

where $M_B$ is the multiplication operator defined by $B$ on the Bergman space $L_a^2(\mathbb{D})$ over the unit disk $\mathbb{D}$. A key result establishes that the number of minimal projections in $\mathcal{V}^*(B)$ equals the number of components of the Riemann surface $ \mathcal{S}_B $ lying in $ \mathbb{D}^2 $. However, computing this integer for a given finite Blaschke product $ B$ remains nontrivial. Traditional methods typically rely on analyzing neighborhoods of the unit circle.

In contrast, our approach leverages the analytic continuations of $ B$ by examining its critical points. This reveals connections between function theory, operator theory, and complex geometry.

This research is a collaborative effort with Danni Guo, Shan Li, Shuaibing Luo.

主讲人简介：

黄寒松，华东理工大学数学学院教授，研究兴趣为函数空间上的算子理论，特别在Bergman空间上的乘法算子理论方面取得了一定的成果。2009年博士毕业于复旦大学数学科学学院，同年进入华东理工大学工作至今。2014.8-2015.8在美国范德堡大学访学，2016年在上海数学中心访问。在Proc. London Math. Soc.; J. Funct. Anal.; J. Geom. Anal.; Sci. China Math.等国内外学术期刊发表科研论文多篇。累计主持并完成国家自然科学基金数项。