报告人：黄寒松 教授（华东理工大学）

时间：2025年07月10日 15:30-

地点：数统学院LD402

摘要：For a finite Blaschke product $B$, it is known that the von Neumann algebra $\mathcal{V}^*(B) =\{M_B,M_B^*\}'$ is abelian, where $M_B$ is the multiplication operator defined by $B$ on the Bergman space $L_a^2(\mathbb{D})$ over the unit disk $\mathbb{D}$. It was proven that the number of minimal projections in $\mathcal{V}^*(B)$ is equal to that of components of the Riemann surface $\mathcal{S}_B$ contained in $\mathbb{D}^2.$ However, determining this integer for a specific finite Blaschke product $B$ is a challenging task. To attack this problem, we develop new techniques in the theory of analytic continuation, and introduce the notion of last components of a finite Blaschke product $B$. The conventional approach involves conducting analysis in a neighborhood of the unit circle. In this talk, however, we analyze the analytic continuations by detecting the critical points of $B$. Consequently, we demonstrate an interplay between function theory, operator theory, and complex geometry.

          This is a joint work with Danni Guo, Shan Li, Shuaibing Luo.

邀请人：数学研究中心

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