Algebraic analysis of integrable hierarchies I
Among integrable systems the KP hierarchy and its cousins are quite important. The solution spaces of them are (infinite dimensional) algebraic varieties and have infinite dimensional symmetries. In this lecture, following Sato's original idea, we show how the solution space of the KP hierarchy is related to an infinite dimensional Grassmann manifold. If the time permits, we will study other hierarchies (the mKP hierarchy, the Toda lattice hierarchy) as well.
讲师
日期
2024年09月09日 至 12月09日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周五 | 09:50 - 11:25 | A3-3-201 | ZOOM 02 | 518 868 7656 | BIMSA |
修课要求
Undergraduate analysis and algebra.
课程大纲
1. Introduction (incomplete history of soliton theory)
2. Microdifferential operators
3. KP hierarchy
4. Finite dimensional Grassmann manifolds and differential equations
5. Sato Grassmannian
6. Sato Grassmannian and microdifferential operators
7. KP hierarchy as a dynamical system on the Sato Grassmannian
2. Microdifferential operators
3. KP hierarchy
4. Finite dimensional Grassmann manifolds and differential equations
5. Sato Grassmannian
6. Sato Grassmannian and microdifferential operators
7. KP hierarchy as a dynamical system on the Sato Grassmannian
参考资料
Miwa, T., Jimbo, M. and Date, E., Solitons —Differential equations, symmetries and infinite-dimensional algebras—. Iwanami, Tokyo, (1993), in Japanese; Engl. translation. Cambridge Tracts in Mathematics, 135. Cambridge University Press, Cambridge, (2000).
Sato, M and Noumi, M, Soliton Equations and Universal Grassmann Manifold, (in Japanese), Sophia University, Tokyo, Mathematical Lecture Note 18, (1984)
https://digital-archives.sophia.ac.jp/repository/view/repository/20200107004?lang=en
Sato Mikio Lecture Notes (note taken by Umeda), RIMS Lecture Notes 5, Kyoto University,
https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/215756?locale=en
Sato, M and Noumi, M, Soliton Equations and Universal Grassmann Manifold, (in Japanese), Sophia University, Tokyo, Mathematical Lecture Note 18, (1984)
https://digital-archives.sophia.ac.jp/repository/view/repository/20200107004?lang=en
Sato Mikio Lecture Notes (note taken by Umeda), RIMS Lecture Notes 5, Kyoto University,
https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/215756?locale=en
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Takashi Takebe 从事数学物理可积系统方向的研究。 2023年8月前，他在俄罗斯莫斯科国立研究大学高等经济学院数学系担任教授，并于2023年9月加入北京雁栖湖应用数学研究院任研究员一职。