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H 1 Geometric quantization of toric and semitoric systems

Auteurs : Miranda, Eva (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : One of the many contributions of Kostant is a rare gem which probably has not been 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 the number of integer points inside the corresponding Delzant 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.

    Keywords : geometric quantization; Kostant's model; polarization; Bohr-Sommerfeld leaf; Delzant polytope; foliation; toric manifold

    Codes MSC :
    53D50 - Geometric quantization

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 18/10/2018
      Date de captation : 08/10/2018
      Collection : Research talks
      Sous collection : Research talks
      Format : MP4
      Durée : 00:55:06
      Domaine : Topology ; Mathematical Physics ; Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-10-08_Miranda.mp4

    Informations sur la rencontre

    Nom de la rencontre : International workshop on geometric quantization and applications / Colloque international "Quantification géométrique et applications"
    Organisateurs de la rencontre : Ma, Xiaonan ; Meinrenken, Eckhard ; Paradan, Paul-Emile
    Dates : 08/10/2018 - 12/10/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1867.html

    Citation Data

    DOI : 10.24350/CIRM.V.19464303
    Cite this video as: Miranda, Eva (2018). Geometric quantization of toric and semitoric systems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19464303
    URI : http://dx.doi.org/10.24350/CIRM.V.19464303


    Voir aussi

    Bibliographie

    1. Miranda, E., Presas, F., & Solha, R. (2017). Geometric quantization of semitoric systems and almost toric manifolds. - https://arxiv.org/abs/1705.06572

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