Scientific Goals

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Poisson geometry is the geometry of manifolds equipped with a Poisson bracket, which is an algebraic structure on their space of smooth functions. Many naturally occurring spaces, like phase-spaces in mechanics and the dual of any Lie algebra, have canonical Poisson brackets.

Poisson brackets were discovered by Siméon-Denis Poisson (1781-1840) (click figure), while working on celestial mechanics. Recently, Poisson geometry has developed rapidly due to new and exciting results related to classification of Poisson brackets, deformation quantization, topological invariants and differential equations occurring in mathematical physics. New connections with other areas of mathematics and mathematical physics have given rise to fruitful interactions, advanced our knowledge, and have proved useful in applications.

The Poisson 2002 conference aims at bringing together leading experts in Poisson geometry and related fields, as well as young researchers who have already made promising contributions, thus meeting the need for a forum to cover recent progress and to stimulate exchanges among active researchers. This conference will cover the following areas of Poisson geometry: local properties (singularities of Poisson structures, linear approximations), hamiltonian systems (moment maps), global geometry (Poisson-Lie groups, Poisson G-spaces, Poisson super geometry, quasi-Poisson manifolds) and Poisson topology (modular class, characteristic classes and other invariants, K-theory, integrability of Poisson manifolds). Related fields that will also be touched upon in this conference include: symplectic and related geometries, integrable systems, deformation and geometric quantization, Lie algebroids and groupoids, quantum field theory.