广州数学大讲坛第三期

第二十四讲——华东理工大学黄寒松教授学术报告

题目：On multiplication operators defined by finite Blaschke products over the Bergman space via critical points

时间：2025年4月12日（星期六）下午15:30-17:00

地点：理学实验楼314

报告人：黄寒松 教授

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. 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.

报告人简介：

黄寒松，华东理工大学快猫app 教授，研究兴趣为函数空间上的算子理论，特别是在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.、Adv. Math.、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。主持并完成国家自然科学基金数项。