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Critical phenomena in random matrix theory and integrable systems

Objective

The main goal of the project is to create a research group on critical phenomena in random matrix theory and integrable systems at the Université Catholique de Louvain, where the PI was recently appointed.
Random matrix ensembles, integrable partial differential equations and Toeplitz determinants will be the main research topics in the project. Those three models show intimate connections and they all share certain properties that are, to a large extent, universal. In the recent past it has been showed that Painlevé equations play an important and universal role in the description of critical behaviour in each of these areas. In random matrix theory, they describe the local correlations between eigenvalues in appropriate double scaling limits; for integrable partial differential equations such as the Korteweg-de Vries equation and the nonlinear Schrödinger equation, they arise near points of gradient catastrophe in the small dispersion limit; for Toeplitz determinants they describe phase transitions for underlying models in statistical physics.
The aim of the project is to study new types of critical behaviour and to obtain a better understanding of the remarkable similarities between random matrices on one hand and integrable partial differential equations on the other hand. The focus will be on asymptotic questions, and one of the tools we plan to use is the Deift/Zhou steepest descent method to obtain asymptotics for Riemann-Hilbert problems. Although many of the problems in this project have their origin or motivation in mathematical physics, the proposed techniques are mostly based on complex and classical analysis.

Call for proposal

ERC-2012-StG_20111012
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

UNIVERSITE CATHOLIQUE DE LOUVAIN
Address
Place De L Universite 1
1348 Louvain La Neuve
Belgium
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 130 400
Principal investigator
Tom Claeys (Prof.)
Administrative Contact
Anne Bovy (Mrs.)

Beneficiaries (1)

UNIVERSITE CATHOLIQUE DE LOUVAIN
Belgium
EU contribution
€ 1 130 400
Address
Place De L Universite 1
1348 Louvain La Neuve
Activity type
Higher or Secondary Education Establishments
Principal investigator
Tom Claeys (Prof.)
Administrative Contact
Anne Bovy (Mrs.)