Marie Curie Action IRSES
International Research Staff Exchange Scheme
RIMMP - Random and Integrable Models in Mathematical Physics
Project Coordinator:
T.
Grava
Starting
date: 1 December 2010
Project
summary: The main goal of the present project is to put the
theory of random matrices, random permutations and random walks in
the context of the theory of integrable systems. This goal will be
achieved by a significant progress in the theory of integrable
systems and their perturbations, including its analytic, geometric
and numerical aspects. Numerical methods will play a particularly
important role in the realization of this programme since they can be
used to visualize problems, to come up with new conjectures and even
to indicate directions along which to prove them. In this project,
the numerical work is very closely accompanied with the analytical
work. The systematic numerical study of oscillatory regimes and break
up and blow up behaviour will provide conjectures for the analytical
description, and add strong quantitative support to found
conjectures. This will help finding approaches to prove theorems. On
the other hand, analytical knowledge will be used as much as possible
to develop efficient algorithms. We plan that all codes developed
during this project will be made freely available to the community.
This will make the state of the art in scientific computing
accessible for the community working on random matrices, Painlevé
transcendents and integrable and non-integrable dispersive PDE.
Partners:
Mathematical Physics Sector, SISSA, Italy. Researchers: B. Dubrovin, G. Falqui, T. Grava
Department of Mathematics, Katholieke Universiteit Leuven, Belgium. Researchers: T. Claeys, A. Kuijlaars, W. Van Assche
Department of Mathematics, Tsinghua University, China. Researchers: , Y. Zhang, Si-Qi Liu
School of Mathematics and Statistics, University of Sydney, Australia. Researchers: N. Joshi, J. Atkinson
Department of Mathematics and Statistics, University of Otago, New Zealand. Researcher: J. Frauendiener
Department of Mathematical Sciences, Brunel University West London, United Kingdom. Researcher: I. Krasovsky
Department of Mathematics, Indiana University - Purdue University Indianapolis, USA. Researchers: P. Bleher, A. Its
Centre de Recherches Mathematiques, Université de Montreal, Canada. Researchers: M. Bertola, D. Korotkin, V. Shramchenko
Institut de Mathématique de Bourgogne, Université de Bourgogne, France. Researcher: C. Klein
Department of Mathematics, University of Arizona, USA. Researcher: K. Mclaughlin
Centre National Recherches Scientifique, Université François-Rabelais de Tours, France. Researcher: O. Lisovy