Integrable Hierarchies & Geometry
Develop the geometric organization of commuting flows, spectral data and algebraically integrable systems.
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
Hierarchies & commuting flows
Planned coverage
- The KP and Toda hierarchies
CHAPTER 02
Bi-Hamiltonian structures & recursion operators
Planned coverage
- The Lenard–Magri recursion
CHAPTER 03
Tau functions, bilinear identities & Grassmannians
Planned coverage
- The Sato Grassmannian
CHAPTER 04
Spectral curves & finite-gap integration
Planned coverage
- Finite-gap solutions and theta functions
CHAPTER 05
Algebraic integrability & Hitchin systems
Planned coverage
- Hitchin fibrations and spectral curves
CHAPTER 06
Dispersionless hierarchies & Frobenius geometry
Planned coverage
- Frobenius manifolds and principal hierarchies
CHAPTER 07
Integrable differential geometry
Planned coverage
- Curved flats and integrable surface equations
CHAPTER 08
Matrix models & topological recursion
Planned coverage
- Spectral curves and topological recursion