Orateur : Pierre Bieliavsky (Université catholique de Louvain)

Résumé

The talk will be addressed to a general audience of mathematicians. I will present some differential geometric aspects of quantization and describe their involvement in Lie theory, harmonic analysis and operator algebras. By quantization, I mean a correspondence which associates to a classical observable, i.e. a scalar function on a the phase space  of a physical system (with a finite number of degree of freedom), an operator on a certain hilbert space which describe the observable at the quantum level, that is, when the physical system is considered at the microscopic level : at a scale where classical  mechanics (symplectic geometry) does not describe its behaviour anymore. By geometry, I mean the geometry induced by the datum of a linear connection (e.g. geodesics, curvature and so on)  on the symplectic manifold constituted by the phase space of our physical system. I will in particular argue that the dynamics of the system often yields, quite canonically, such a connection, or rather a family of those.          

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