2024年第8期第77讲：赵翀教授学术报告

广州数学大讲坛第八期

第七十七讲——山东大学赵翀教授学术报告

题目：双圆盘Hardy商模的本质正规性和子模的Hilbert-Schmidt性

时间：2024年11月19日（星期二）下午14：30-15：30

地点：腾讯会议（会议ID：914-706-949，密码：241119）

报告人：赵翀 教授

摘要：I would like to talk our latest work on the essential normality of quotient modules over the polydiscs, and the Hilbert-Schmidtness of submodules. We prove that all the quotient modules in H²(D²), associated to the finitely generated submodules containing a distinguished homogenous polynomial, are essentially normal, which is the first result on the essential normality of non-algebraic quotient modules in H²(D²). Moreover, we obtain the equivalence of the essential normality of a quotient module and the Hilbert-Schmidtness of its associated submodule in H²(D²), in the case that the submodule contains a distinguished homogenous polynomial. As an application, we prove that each finitely generated submodule containing a polynomial is Hilbert-Schmidt, which partially gives an affirmative answer to a conjecture of R. Yang.

报告人简介：

赵翀，山东大学教授，2014年于复旦大学获得理学博士学位。研究方向为算子理论与算子代数，主要课题为复单位球和多圆盘上Hilbert模的本质正规性。近年来与合作者在多圆盘上的系列工作给出了（拟）齐次商模本质正规性的完全判别准则，完整回答了多圆盘上相应的Arveson问题。相关论文发表于Adv. Math., J. London Math. Soc., Sci. China. Math. 等数学期刊。目前主持国家自然科学基金面上项目一项。