主 讲 人 ：谢玉芳    

活动时间：2025-05-29 16:30:00

地      点 ：理科群1号楼D203室 https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1 会议 ID: 86763384947；密码: 612593

主办单位：数学科学学院

讲座内容：

Let $\mathcal{H}$ be a complex separable Hilbert space. For $\Omega$ an open connected subset of $\mathbb{C}$, we shall say that a map $f:\Omega\rightarrow \mathrm{Gr}(n,\mathcal{H})$ is a holomorphic curve if there exist $n$ holomorphic $\mathcal{H}$-valued functions $\gamma_{1},\gamma_{2},\ldots,\gamma_{n}$ on $\Omega$ such that

$$f(w)=\bigvee\{\gamma_{1}(w),\gamma_{2}(w),\ldots,\gamma_{n}(w)\},$$

where $\mathrm{Gr}(n, \mathcal{H})$ denotes the Grassmann manifold, i.e., the set of all $n$-dimensional subspaces of $\mathcal{H}$.

Homogeneous and weakly homogeneous curves in the Cowen-Douglas class were introduced by A. Korányi and G. Misra. Research on such curves has revealed deep connections among group representation theory, Hilbert modules, and complex geometry.

In this talk, we introduce a new and broad class of holomorphic curves, which includes both homogeneous and weakly homogeneous cases. Using certain geometric invariants, we also present a similarity classification theorem for this class of curves.

主讲人介绍：

The speaker is a third-year Master's student at the School of Mathematical Sciences, Hebei Normal University. Her research mainly focuses on the intersection of operator theory and complex geometry under the supervision of Professor Kui Ji.