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H 1 On the proof of S-duality modularity conjecture on quintic threefolds

Auteurs : Sheshmani, Artan (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will talk about joint work during the recent years with Amin Gholampour, Richard Thomas and Yukinobu Toda, on proving the modularity property of the generating series of certain DT invariants of torsion sheaves with two dimensional support in ambient threefolds. More specifically, I will talk about algebraic-geometric proof of S-duality conjecture in superstring theory made formerly by physicists: Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hibert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson for absolute Hilbert schemes. These intersection numbers, together with the generating series of Noether-Lefschetz numbers, will provide the ingrediants to prove modularity of the above DT invariants over the quintic threefold.

    Codes MSC :
    14J30 - 3-folds [See also 32Q25]
    14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
    81T30 - String and superstring theories; other extended objects (e.g., branes)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 02/12/15
      Date de captation : 27/10/15
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 01:04:27
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-10-27_Sheshmani.mp4

    Informations sur la rencontre

    Nom de la rencontre : Moduli spaces in geometry / Espaces de modules en géométrie
    Organisateurs de la rencontre : Ayoub, Joseph ; Schmitt, Alexander ; Teleman, Andrei
    Dates : 26/10/15 - 30/10/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1139.html

    Citation Data

    DOI : 10.24350/CIRM.V.18868203
    Cite this video as: Sheshmani, Artan (2015). On the proof of S-duality modularity conjecture on quintic threefolds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18868203
    URI : http://dx.doi.org/10.24350/CIRM.V.18868203


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