**CRM Proceedings & Lecture Notes**

Volume: 31;
2002;
218 pp;
Softcover

MSC: Primary 34; 35; 58; 81; 30; 33;

Print ISBN: 978-0-8218-2804-5

Product Code: CRMP/31

List Price: $78.00

Individual Member Price: $62.40

**Electronic ISBN: 978-1-4704-3945-3
Product Code: CRMP/31.E**

List Price: $78.00

Individual Member Price: $62.40

# Isomonodromic Deformations and Applications in Physics

Share this page *Edited by *
*John Harnad; Alexander Its*

A co-publication of the AMS and Centre de Recherches Mathématiques

The area of inverse scattering transform method or soliton theory has evolved
over the past two decades in a vast variety of exciting new algebraic and
analytic directions and has found numerous new applications. Methods and
applications range from quantum group theory and exactly solvable statistical
models to random matrices, random permutations, and number theory. The theory
of isomonodromic deformations of systems of differential equations with
rational coefficents, and most notably, the related apparatus of the
Riemann-Hilbert problem, underlie the analytic side of this striking
development.

The contributions in this volume are based on lectures given by leading
experts at the CRM workshop (Montreal, Canada). Included are both survey
articles and more detailed expositions relating to the theory of isomonodromic
deformations, the Riemann-Hilbert problem, and modern applications.

The first part of the book represents the mathematical aspects of
isomonodromic deformations; the second part deals mostly with the various
appearances of isomonodromic deformations and Riemann-Hilbert methods in the
theory of exactly solvable quantum field theory and statistical mechanical
models, and related issues. The book elucidates for the first time in the
current literature the important role that isomonodromic deformations play in
the theory of integrable systems and their applications to physics.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students, research mathematicians, and physicists.

# Table of Contents

## Isomonodromic Deformations and Applications in Physics

- Cover Cover11
- Title page iii4
- Contents v6
- Frontispiece vii8
- List of participants ix10
- Preface xiii14
- Isomonodromic Deformations 118
- Inverse problems for linear differential equations with meromorphic coefficients 320
- Virasoro generators and bilinear equations for isomonodromic tau functions 2744
- Lax pairs for Painlevé equations 3754
- Isomonodromic deformations and Hurwitz spaces 4966
- Classical solutions of Schlesinger equations and twistor theory 6178
- 𝑊-geometry and isomonodromic deformations 6986
- Airy kernel and Painlevé II 85102
- Applications in Physics and Related Topics 97114
- Jacobi groups, Jacobi forms and their applications 99116
- Symmetry, the Chazy equation and Chazy hierarchies 113130
- Universal correlations of one-dimensional electrons at low density 131148
- A quantum version of the inverse scattering transformation 149166
- Continued fractions and integrable systems 163180
- Hypergeometric functions related to Schur functions and integrable systems 175192
- Ising model scaling functions at short distance 195212
- The partition function of the six-vertex model as a Fredholm determinant 207224
- Back Cover Back Cover1236