CRM Proceedings & Lecture Notes 2002; 218 pp; softcover Volume: 31 ISBN10: 0821828045 ISBN13: 9780821828045 List Price: US$78 Member Price: US$62.40 Order Code: CRMP/31
 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 RiemannHilbert 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 RiemannHilbert 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 RiemannHilbert 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 copublished 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 onedimensional 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 sixvertex model as a Fredholm determinant
