Isomonodromic deformations and tau functions
I will talk about a general theory of monodromy preserving deformation, which is developed for a system of linear ordinary differential
equations dY/dx = A(x)Y, where A(x) is a rational matrix. In the first part, I will talk about the asymptotic solutions for the equation with regular and irregular singularities respectively, then the corresponding monodromy data including connection matrix, Stokes matrix and so on. In the second part, I will talk about the equations of isomonodromic deformation and assoicatied tau function, which plays a central role in the deformation theory. For example, in the special case (studied by Riemann), the tau function reduces to the theta functions. I will also talk about Schlesinger transformation and Characterisitic matrix in the theory of tau function. Finally, I will talk about its applications on the model of mathematical physics.
equations dY/dx = A(x)Y, where A(x) is a rational matrix. In the first part, I will talk about the asymptotic solutions for the equation with regular and irregular singularities respectively, then the corresponding monodromy data including connection matrix, Stokes matrix and so on. In the second part, I will talk about the equations of isomonodromic deformation and assoicatied tau function, which plays a central role in the deformation theory. For example, in the special case (studied by Riemann), the tau function reduces to the theta functions. I will also talk about Schlesinger transformation and Characterisitic matrix in the theory of tau function. Finally, I will talk about its applications on the model of mathematical physics.
讲师
日期
2023年02月27日 至 05月22日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 15:20 - 18:40 | A3-2-201 | ZOOM 06 | 537 192 5549 | BIMSA |
修课要求
basic knowledge of function of one complex variable, algebraic topology, compact Riemann surface
参考资料
1. Michio JIMBO, Tetsuji MIWA and Kimio UENO; Monodromy preserving deformation of linear ordinary differential equations with rational coefficient I. general theory and tau functions
2. Michio JIMBO and Tetsuji MIWA; Monodromy preserving deformation of linear ordinary differential equations with rational coefficient II
3. Michio JIMBO and Tetsuji MIWA; Monodromy preserving deformation of linear ordinary differential equations with rational coefficient III
2. Michio JIMBO and Tetsuji MIWA; Monodromy preserving deformation of linear ordinary differential equations with rational coefficient II
3. Michio JIMBO and Tetsuji MIWA; Monodromy preserving deformation of linear ordinary differential equations with rational coefficient III
听众
Graduate
视频公开
不公开
笔记公开
公开
语言
中文
讲师介绍
2013于四川大学数学学院基础数学专业获学士学位，2018年于北京大学北京国际数学研究中心获博士学位，2018-2021在清华大学丘成桐数学科学中心做博士后，2021年加入北京雁栖湖应用数学研究院任助理研究员。研究兴趣包括：可积系统，特别是GW理论、LG理论中出现的无穷维可积系统，兴趣在于理解其中的无穷个对称性的代数结构和相关计算。其他兴趣还包括：混合Hodge结构、等单值形变理论、KZ方程。