Isomonodromy & Special Functions
Develop monodromy-preserving problems, nonlinear special functions and exact differential-equation spectral methods.
This volume will develop the subjects in the chapter map below. Use the outline to locate the methods and examples you want to study; the individual readings are still being developed.
Learning sequences: Open Toda · The XXX spin chain · KdV solitons · Finite-ring TASEP
Readings and planned coverage
CHAPTER 01
Monodromy, Stokes data & linear systems
Planned coverage
- Stokes matrices and connection data
CHAPTER 02
Isomonodromic deformations
Planned coverage
- Schlesinger equations
CHAPTER 03
Painlevé & Garnier systems
Planned coverage
- Painlevé equations and Hamiltonian formulations
CHAPTER 04
Tau functions & connection problems
Planned coverage
- Isomonodromic tau functions
CHAPTER 05
The ODE/IM correspondence
Planned coverage
- Spectral determinants in ODE/IM
CHAPTER 06
Exact WKB & resurgence
Planned coverage
- Exact WKB connection formulas
CHAPTER 07
Special functions & exact spectral problems
Planned coverage
- Heun equations in integrable spectral problems