Spectra of the Darboux–Treibich–Verdier operators
This course will study the spectrum of the Schrödinger operator with Darboux– Treibich–Verdier (DTV) potential. The DTV potential first discovered by Darboux in 1882 and rediscovered by Trebich and Verdier in 1988, represents a remarkable doubly periodic solution of stationary KdV hierarchy equations labeled by four integers.
讲师
日期
2023年09月22日 至 2024年01月19日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周五 | 09:50 - 12:15 | A3-2-303 | ZOOM 02 | 518 868 7656 | BIMSA |
修课要求
Calculus, Linear algebra
课程大纲
1. Introduction
2. Ordinary differential equations with regular singularities
3. Floquet Theory
4. KdV potentials
5. Spectral Theory of Hill’s equations
6. Spectra of the DTV operators
2. Ordinary differential equations with regular singularities
3. Floquet Theory
4. KdV potentials
5. Spectral Theory of Hill’s equations
6. Spectra of the DTV operators
参考资料
[1] Z. Chen, E. Fu and C. S. Lin; A necessary and sufficient condition for the Darboux-TreibichVerdier potential with its spectrum contained in ℝ. Amer. J. Math. 144 (2022), no. 3, 851–87
[2] F. Gesztesy and H. Holden; Soliton equations and their algebro-geometric solutions. Vol. I. (1 + 1)-dimensional continuous models. Cambridge Studies in Advanced Mathematics, vol. 79, Cambridge University Press, Cambridge, 2003. xii+505 pp.
[3] Wilhelm Magnus and Stanley Winkler; Hill’s equation. (Corrected reprint of the 1966 edition) Dover Publications, Inc., New York (1979) viii+129.
[2] F. Gesztesy and H. Holden; Soliton equations and their algebro-geometric solutions. Vol. I. (1 + 1)-dimensional continuous models. Cambridge Studies in Advanced Mathematics, vol. 79, Cambridge University Press, Cambridge, 2003. xii+505 pp.
[3] Wilhelm Magnus and Stanley Winkler; Hill’s equation. (Corrected reprint of the 1966 edition) Dover Publications, Inc., New York (1979) viii+129.
听众
Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
中文
讲师介绍
2019年在Yuan Pin Lee和Herb Clemens的指导下获得了犹他大学的博士学位；后于清华大学丘成桐数学科学中心做博士后。2022年12月加入北京雁栖湖应用数学研究院任助理研究员。目前研究Darboux Treibich Verdier算子的谱和相关问题。