On Infinite Periodic Band Matrices and the Periodic Toda Flow
数学专题报告
报告题目(Title)：On Infinite Periodic Band Matrices and the Periodic Toda Flow
报告人(Speaker)：Prof. Li Luen-Chau（宾夕法尼亚州立大学）
地点(Place)：后主楼1225
时间(Time)：2025年12月30日（周二）9:00-10:00
邀请人(Inviter)：孙若词、王灯山
报告摘要
In this talk, we will consider an isospectral deformation of infinite periodic band matrices with period n, with lower bandwidth equal to k, and upper bandwidth equal to k_0 , and subject to the conditions that 1 ≤ k, k_0 ≤ n−1, k + k_0 < n. We will show that this flow, which was introduced by van Moerbeke and Mumford in the late 1970s, translates into a corresponding flow on matrix loops in gl(n, C), which turns out to be a natural extension of the periodic full Kostant-Toda flow introduced by Ben-Adeljelil. We will then show that this flow is Liouville integrable on generic coadjoint orbits of an infinite-dimensional Lie group. Finally, we will discuss the correspondence between an open collection of loops corresponding to the infinite periodic band matrices, and the collection of extended algebro-geometric data. The additional variables in the extended algebro-geometric data allow us to set up a bijection between the two sets of objects, thus extending the dictionary in the work of van Moerbeke and Mumford.
主讲人简介
Li Luen-Chau（宾夕法尼亚州立大学教授），博士毕业于New York University, 师从Percy Deift教授。研究领域包含可积系统，Poisson几何和数学物理。目前已在高水平期刊Commun. Pure Appl. Math., Commun. Math. Phys.等发表多篇论文。
