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Isomonodromic Deformations and Applications in Physics
Edited by: John Harnad, University of Montreal, QC, Canada, and Alexander Its, Indiana University - Purdue University, Indianapolis, IN
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Proceedings & Lecture Notes
2002; 218 pp; softcover
Volume: 31
ISBN-10: 0-8218-2804-5
ISBN-13: 978-0-8218-2804-5
List Price: US$74
Member Price: US$59.20
Order Code: CRMP/31
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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
  • A. Bolibruch -- Inverse problems for linear differential equations with meromorphic coefficients
  • J. Harnad -- Virasoro generators and bilinear equations for isomonodromic tau functions
  • A. A. Kapaev -- Lax pairs for Painlevé equations
  • D. A. Korotkin -- Isomonodromic deformations and Hurwitz spaces
  • Y. Ohyama -- Classical solutions of Schlesinger equations and twistor theory
  • M. A. Olshanetsky -- \(W\)-geometry and isomonodromic deformations
  • C. A. Tracy and H. Widom -- Airy kernel and Painlevé II
Applications in Physics and Related Topics
  • M. Bertola -- Jacobi groups, Jacobi forms and their applications
  • P. A. Clarkson and C. M. Cosgrove -- Symmetry, the Chazy equation and Chazy hierarchies
  • F. Göhmann -- Universal correlations of one-dimensional electrons at low density
  • F. Göhmann and V. E. Korepin -- A quantum version of the inverse scattering transformation
  • Y. Nakamura -- Continued fractions and integrable systems
  • A. Yu. Orlov and D. M. Scherbin -- Hypergeometric functions related to Schur functions and integrable systems
  • J. Palmer -- Ising model scaling functions at short distance
  • N. A. Slavnov -- The partition function of the six-vertex model as a Fredholm determinant
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