Research project P7/18 (Research action P7)
The project concerns the study of scaling limits and, reversely, deformations of systems of related but different natures:
• Dynamical systems and stochastic processes in the framework of statistical mechanics;
• Critical phenomena of dynamical systems and random matrices;
• Various types of algebras related to symplectic manifolds.
The project is interdisciplinary as it involves physicists and mathematicians with different backgrounds. One of its main goals is to promote cross-fertilization between the above-mentioned approaches.
The network brings together mathematicians and mathematical and statistical physicists, among which are two recipients of the Francqui Prize (Pierre Gaspard, Pierre Van Moerbeke), four ERC starting grant holders: Frédéric Bourgeois, Pierre-Emmanuel Caprace, Tom Claeys and Stefaan Vaes, and one ERC grant holder (Stefano Olla, International partner at Paris Dauphine). Stefaan Vaes and Arno Kuijlaars were invited speakers at the last ICM. Jean Bricmont is recipient of a Prix quinquennal du FNRS. This network is partly new, consisting of the nodes of an IAP network of the current phase (06/02--Nonlinear systems, stochastics processes and statistical mechanics) namely UCL, ULB (Pierre Gaspard), KULeuven and two new nodes ULB (Frédéric Bourgeois) and ULg.
The network comprises three workpackages:
• Work-package 1 : Nonlinear dynamics and statistical mechanics : ULB, UCL, KULeuven
• Work-package 2 : Dynamical and Integrable Systems : KULeuven, UCL
• Work-package 3 : Symplectic geometry, homological methods and operator algebras : KULeuven, UCL,ULg, ULB.
Work-package 1 is a continuation of the work undertaken in the network IAP 06/02, merging its WPs 2 and 4.
A main feature of the work-package 2 on Dynamical and Integrable Systems is the recent appointment of a young and very promising faculty member at UCL (Tom Claeys).This creates a strong momentum and opportunity for collaborative research. WP2 is a continuation of the work undertaken in the network IAP 06/02, merging its WPs 1, 3 and 5.
The Work-package 3 is new and involves world experts in the relevant domains including Bourgeois, Caprace and Vaes. Long term collaborations between members of the WP3 already exist (Pierre Bieliavky (UCL), Mélanie Bertelson, Michel Cahen, Simone Gutt (ULB).