Summary
The main goal of the project will be to establish and explore the bridge between the geometry of the theory of integrable systems and its asymptotic aspects; these results will have an impact on physics, applied mathematics and statistics. To this end, we plan on investigating the relationships, discovered recently by mathematicians and physicists, between integrable differential equations, the topology of Deligne - Mumford moduli spaces and singularity theory. The methods developed will be extended to the study of local normal forms of integrable PDEs in the vicinity of a finite-dimensional invariant manifold and, more generally, to the analysis of properties of asymptotically integrable systems and their solutions. The results in this study, together with techniques borrowed from analysis and infinite-dimensional Lie algebras, have many applications: (i) to questions on random matrices, random permutations and random walks, (ii) to constructions of asymptotic solutions to classical and quantum systems, both discrete and continuous. European researchers are actively involved in the study of these problems. The main scope of the Programme is to unify the European efforts on this exciting interdisciplinary project and to create a fruitful training ground for young researchers.
Keywords:
Classical and quantum integrable systems
Gromow-Witten invariants
Random Matrices
Singularity theory
Weakly dispersive waves
The programme proposal was originally submitted by Professor Pierre van Moerbecke (Université de Louvain, Belgium) and Professor Boris Dubrovin (SISSA, Trieste).
For more information, please go to the programme’s homepage go to website
Duration
Five years from July 2004 until July 2009
