Algebraic and Geometric Aspects of Integrable Systems and Random Matrices
About this Title
Anton Dzhamay, University of Northern Colorado, Greeley, CO, Kenichi Maruno, University of Texas-Pan American, Edinburg, TX and Virgil U. Pierce, University of Texas-Pan American, Edinburg, TX, Editors
Publication: Contemporary Mathematics
Publication Year 2013: Volume 593
ISBNs: 978-0-8218-8747-9 (print); 978-1-4704-0991-3 (online)
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6–7, 2012, in Boston, MA.
The very wide range of topics represented in this volume illustrates the importance of methods and ideas originating in the theory of integrable systems to such diverse areas of mathematics as algebraic geometry, combinatorics, and probability theory. The volume offers a balanced combination of survey articles and research papers with important new results.
Graduate students and research mathematicians interested in the various aspects of the theory of integrable systems and its applications, including connections with the theory of random matrices and map enumeration.
Table of Contents
- Mark Adler, Mattia Cafasso and Pierre van Moerbeke – Nonlinear PDEs for Fredholm determinants arising from string equations
- Jeffery C. DiFranco and Peter D. Miller – The semiclassical modified nonlinear Schrödinger equation II: Asymptotic analysis of the Cauchy problem. The elliptic region for transsonic initial data
- Jacek Szmigielski and Lingjun Zhou – Peakon-antipeakon interactions in the Degasperis-Procesi equation
- Alex Kasman – Duality and collisions of harmonically constrained Calogero particles
- Takao Suzuki – A class of higher order Painlevé systems arising from integrable hierarchies of type $A$
- Hiroshi Kawakami, Akane Nakamura and Hidetaka Sakai – Toward a classification of four-dimensional Painlevé-type equations
- Yousuke Ohyama and Shoji Okumura – R. Fuchs’ problem of the Painlevé equations from the first to the fifth
- Sarbarish Chakravarty – Differential equations for triangle groups
- Adam Doliwa – Hirota equation and the quantum plane
- A. S. Carstea – On the geometry of $Q_4$ mapping
- D. Korotkin and P. Zograf – Tau function and the Prym class
- Olivia Dumitrescu, Motohico Mulase, Brad Safnuk and Adam Sorkin – The spectral curve of the Eynard-Orantin recursion via the Laplace transform
- Virgil U. Pierce – Continuum limits of Toda lattices for map enumeration