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