报告题目：Hilbert-Schmidt norm conjecture of homogeneous polynomial submodules in Hardy space over the bidisk

报告人：祖超

报告人简介：祖超，大连理工大学博士后，2023年在大连理工大学获理学博士学位，2024-04-2025-04在纽约州立大学奥尔巴尼分校数学与统计系交流访问。目前主要从事泛函分析与函数空间上的算子理论方向的研究，已在Journal of Functional Aanalysis,Indiana University Mathematics Journal,Studia Mathematica等国际权威期刊发表多篇学术论文。

报告内容简介：In this talk, we will give a negative answer to the boundedness conjecture of Hilbert-Schmidt norm for rank one submodules in Hardy space over the bidisk. For the homogeneous polynomial submodules $[(z-w)^k]$, by using the results about certain Toeplitz determinants, we show that the corresponding core operator $C$ has eigenvalues $0,1,\pm \frac{k}{n+k}, n\geq 1$. It implies that $2k-1<\|C\|_{H.S.}^2<2k+1$, which tends to infinity when $k$ tends to infinity. Moreover, we find that there is a close connection between the Hilbert-Schmidt norm estimates for homogeneous polynomial submodules and the Fisher-Hartwig conjecture, which describes the asymptotic behavior of Toeplitz determinants for a class of functions.

报告时间：2025年11月30日14:30

报告地点：实训楼109

欢迎各位老师和同学参加！