Séminaire de Géométrie et Quantification

Eva Miranda

(Universitat Politècnica de Catalunya et Observatoire de Paris)

Lundi 6 novembre 15h30 salle 01, IHP

Titre: Geometric quantization of toric and semitoric systems d'après Kostant

Résumé : One of the many contributions of Bertram Kostant (1928-2017) is a rare gem which probably has not sufficiently explored: a sheaf-theoretical model for geometric quantization associated to real polarizations. Kostant's model works very well for polarizations given by fibrations or fibration-like objects (like integrable systems away from singularities). For toric manifolds where the real polarization is determined by the fibers of the moment map, Kostant's model yields a representation space whose dimension is determined by the integer points inside Delzant's polytope. We will discuss extensions of this model to consider almost toric manifolds and integrable systems with non-degenerate singularities where "unexpected" infinities can show up even if the manifold is compact.

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