RESEARCH SCHOOL — Coulomb Gas, Integrability and Painlevé Equations

Nonlinear integrable systems and their solutions form the core of modern mathematical physics. In recent years, Painlevé's equations have emerged as the core of special function theory. Painlevé equations can be derived from integrable PDEs after scaling reductions. They are also obtained in the matching of asymptotic expansions in the quest to describe critical behaviour in solutions to Hamiltonian PDEs. In this case they play the same role as the Airy function or the Pearcey integral play in the study of the semiclassical limit of the linear Schrodinger equation. Increasingly, as nonlinear science develops, solutions to an extraordinary broas array of scientific problems can be expressed in terms of Painlev? transcendents. The aim of this reserach school is to bring together PhD. students, Postdocs and junior faculty members to focus on the new developements in these fertile lines of research. The proposed format is 4 lectures a day and a free afternoon for discussions.

Topics: Jean-Morlet Chair