**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