Softcover ISBN:  9781470416546 
Product Code:  CONM/651 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470427795 
Product Code:  CONM/651.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470416546 
eBook: ISBN:  9781470427795 
Product Code:  CONM/651.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 
Softcover ISBN:  9781470416546 
Product Code:  CONM/651 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470427795 
Product Code:  CONM/651.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470416546 
eBook ISBN:  9781470427795 
Product Code:  CONM/651.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 651; 2015; 194 ppMSC: Primary 34; 37; 39; 35; 14; 17; 33; 41; 81
This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD.
The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory.
Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.
ReadershipGraduate students and research mathematicians interested in integrable systems.

Table of Contents

Articles

Masatoshi Noumi — Padé Interpolation and Hypergeometric Series

Takao Suzuki — A $q$analogue of the DrinfeldSokolov Hierarchy of Type $A$ and $q$Painlevé System

Hajime Nagoya — Fractional Calculus of Quantum Painlevé Systems of Type $A_l^{(1)}$

Christopher M. Ormerod — Spectral Curves and Discrete Painlevé Equations

Anton Dzhamay and Tomoyuki Takenawa — Geometric Analysis of Reductions from Schlesinger Transformations to Difference Painlevé Equations

Igor Rumanov — Beta Ensembles, Quantum Painlevé Equations and Isomonodromy Systems

B. Prinari and F. Vitale — Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a OneSided NonZero Boundary Condition


Additional Material

RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD.
The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory.
Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.
Graduate students and research mathematicians interested in integrable systems.

Articles

Masatoshi Noumi — Padé Interpolation and Hypergeometric Series

Takao Suzuki — A $q$analogue of the DrinfeldSokolov Hierarchy of Type $A$ and $q$Painlevé System

Hajime Nagoya — Fractional Calculus of Quantum Painlevé Systems of Type $A_l^{(1)}$

Christopher M. Ormerod — Spectral Curves and Discrete Painlevé Equations

Anton Dzhamay and Tomoyuki Takenawa — Geometric Analysis of Reductions from Schlesinger Transformations to Difference Painlevé Equations

Igor Rumanov — Beta Ensembles, Quantum Painlevé Equations and Isomonodromy Systems

B. Prinari and F. Vitale — Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a OneSided NonZero Boundary Condition