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H 1 Semi-infinite Hodge structures in noncommutative geometry

Auteurs : Shklyarov, Dmytro (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Homological mirror symmetry asserts that the connection, discovered by physicists, between a count of rational curves in a Calabi-Yau manifold and period integrals of its mirror should follow from an equivalence between the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. Physicists' observation can be reformulated as, or rather upgraded to, a statement about an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the above assertion would be to try to attach similar Hodge-like data to abstract derived categories. The aim of the talk is to report on some recent progress in this direction and illustrate the approach in the context of what physicists call Landau-Ginzburg B-models.

    Codes MSC :
    14A22 - Noncommutative algebraic geometry
    14F05 - Sheaves, derived categories of sheaves and related constructions
    14J32 - Calabi-Yau manifolds
    16E40 - Hochschild and other homology and cohomology theories for rings
    14J33 - Mirror symmetry

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 24/04/2017
      Date de captation : 12/04/17
      Sous collection : Research talks
      Format : MP4
      arXiv category : Algebraic Geometry
      Domaine : Algebra ; Algebraic & Complex Geometry
      Durée : 01:02:52
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-04-12_Shklyarov.mp4

    Informations sur la rencontre

    Nom de la rencontre : Hodge theory, Stokes phenomenon and applications / Théorie de Hodge, phénomène de Stokes et applications
    Organisateurs de la rencontre : Hertling, Claus ; Sabbah, Claude ; Sevenheck, Christian
    Dates : 10/04/17 - 14/04/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1585.html

    Citation Data

    DOI : 10.24350/CIRM.V.19159003
    Cite this video as: Shklyarov, Dmytro (2017). Semi-infinite Hodge structures in noncommutative geometry. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19159003
    URI : http://dx.doi.org/10.24350/CIRM.V.19159003

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