Séminaire de Géométrie et Quantification
(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
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.