Introduction to p-adic differential equations
In the ultrametric setting, linear differential equations exhibit phenomena not observed in the complex field. Indeed, the solutions to these equations may not converge everywhere, even in the absence of poles. This introduces a non-trivial concept of the radius of convergence, and understanding it allows us to gain several interesting insights about the equation. Notably, it influences the finite dimensionality of de Rham cohomology. The main goal of this course is to introduce the framework of ultrametric differential equations.
讲师
日期
2024年03月21日 至 06月21日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四,周五 | 15:20 - 16:55 | A3-2a-302 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
General algebra, Linear algebra, Galois theory of fields, Metric spaces.
课程大纲
The cours can be divided onto the main following parts:
- Some functional ultrametric analysis;
- Extensions of an ultrametric field;
- Generality on differential modules;
- Radii of convergence of the solutions;
- Decomposition with respect to the radii of convergence of the solutions.
- Some functional ultrametric analysis;
- Extensions of an ultrametric field;
- Generality on differential modules;
- Radii of convergence of the solutions;
- Decomposition with respect to the radii of convergence of the solutions.
参考资料
S. Bosch, U. Güntzer, and R. Remmert. Non-archimedean analysis : a systematic approach to rigid analytic geometry. Grundlehren der mathematischen Wissenschaften, 261. Springer-Verlag, 1984.
K. S. Kedlaya. p-adic differential equations. English. Cambridge: Cam- bridge University Press, 2010.
G. Christol. “Le théorème de turritin p-adique (version du 11/06/2011)”.
G. Christol. “Modules différentiels et équations différentielles p-adiques”. In: Queen’s Papers in Pure and Applied Math (1983).
G. Christol and P. Robba. Équations différentielles p-adiques - Applications aux sommes exponentielles. Actualités Mathématiques. Hermann, 1994.
K. S. Kedlaya. p-adic differential equations. English. Cambridge: Cam- bridge University Press, 2010.
G. Christol. “Le théorème de turritin p-adique (version du 11/06/2011)”.
G. Christol. “Modules différentiels et équations différentielles p-adiques”. In: Queen’s Papers in Pure and Applied Math (1983).
G. Christol and P. Robba. Équations différentielles p-adiques - Applications aux sommes exponentielles. Actualités Mathématiques. Hermann, 1994.
听众
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
I have been an assistant professor at BIMSA since January 2024. My research primarily focuses on p-adic differential equations. I defended my Ph.D. thesis in 2018 at Montpellier University. Before joining BIMSA, I was an assistant professor at Algiers University. Subsequently, I was a postdoc at YMSC, Tsinghua University, from April 2021 to December 2023.