Jean-Michel Bismut (Université Paris-Sud)
Varghese Mathai (University of Adelaide)
Michèle Vergne (Institut Mathématiques de Jussieu)

Xiaonan Ma (Université Paris Diderot)
Eckhard Meinrenken (University of Toronto)
Paul-Emile Paradan (Université de Montpellier)

Nowadays, geometric quantization can be understood in the following general sense. Consider a symmetry group G of a manifold M with a given geometric data Γ. Here Γ can be a symplectic form, a spin c structure, a fibration, etc… Then the aim of geometric quantization is to associate to these data a representation of G in a vector space Q(M, Γ), and to analyze the relationship of the quantum space Q(M, Γ) with the classical data (M, Γ). There are diverse constructions of the quantum space Q(M, Γ) but they should all have the functorial property, summarized by Guillemin-Sternberg’s creed Quantization commutes with Reduction.

Today, geometric quantization continues to be a highly active area, with links to physics, symplectic geometry, representation theory, index theory, differential geometry and geometric analysis. The purpose of the present workshop is to present different facets of the “geometric quantization” theme, including topics such as
– quantization of Hamiltonian manifolds,
– group valued momentum maps,
– moduli space problems,
– branching rules,
– semiclassical asymptotics,
– index theory (Atiyah-Singer and Connes-Kasparov).

This conference will bring together mathematicians working on these topics. The techniques cover a fairly broad spectrum (Ktheory and K-homology, analytical estimates, C*-algebras, representation theory) and the philosophy of geometric quantization will act as a focal point for the interaction between all of these areas. The workshop will provide an excellent opportunity for experts working on different aspects of the theory to exchange ideas, leading to fresh insights and new developments.

Ce colloque rassemblera des mathématiciens travaillant sur ces sujets. Les techniques employées couvrent un spectre assez large (Kthéorie et K-homologie, estimations analytiques, C*-algèbres, théorie des représentations) et la philosophie de la quantification géométrique servira de fil conducteur pour permettre une interaction entre ces différents domaines. Ce colloque offrira une excellente opportunité aux experts travaillant sur différents aspects de la théorie pour échanger des idées, conduisant à de nouvelles perspectives et à de nouveaux développements.