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.
Lecturer
Date
27th February ~ 22nd May, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 15:20 - 18:40 | A3-2-201 | ZOOM 06 | 537 192 5549 | BIMSA |
Prerequisite
basic knowledge of function of one complex variable, algebraic topology, compact Riemann surface
Reference
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
Audience
Graduate
Video Public
No
Notes Public
Yes
Language
Chinese
Lecturer Intro
Xinxing Tang, received a bachelor's degree in basic mathematics from the School of Mathematics, Sichuan University in 2013, and received a doctorate from Beijing International Center for Mathematical Research, Peking University in 2018. From 2018 to 2021, she worked as a postdoctoral fellow at the Yau Mathematical Sciences Center, Tsinghua University, and joined Beijing Institute of Mathematical Sciences and Applications in 2021 as assistant professor. Research interests include: integrable systems, especially infinite-dimensional integrable systems that appear in GW theory and LG theory, and are interested in understanding the algebraic structure of infinite symmetries and related calculations. Other interests include: mixed Hodge structures, isomonodromic deformation theory, KZ equations.