Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations

Ebook Details

Authors

Anton Dzhamay, Kenichi Maruno, Christopher M. Ormerod

Year 2015
Pages 194
Publisher Amer Mathematical Society
Language en
ISBN 9781470416546
File Size 1.42 MB
File Format PDF
Download Counter 100
Amazon Link

Ebook Description

This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painleve 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 Painleve 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.