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H 1 Calabi-Yau manifolds, mirror symmetry, and $F$-theory - part II

Auteurs : Morrison, David R. (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : There are five superstring theories, all formulated in 9+1 spacetime dimensions; lower-dimensional theories are studied by taking some of the spatial dimensions to be compact (and small). One of the remarkable features of this setup is that the same lower-dimensional theory can often be realized by pairing different superstring theories with different geometries. The focus of these lectures will be on the mathematical implications of some of these physical “dualities.”
    Our main focus from the string theory side will be the superstring theories known as type IIA and type IIB. The duality phenomenon occurs for compact spaces of various dimensions and types. We will begin by discussing “T-duality” which uses tori as the compact spaces. We will then digress to introduce M-theory as a strong-coupling limit of the type IIA string theory, and F-theory as a variant of the type IIB string theory whose existence is motivated by T-duality. The next topic is compactifying the type IIA and IIB string theories on K3 surfaces (where the duality involves a change of geometric parameters but not a change of string theory).
    By the third lecture, we will have turned our attention to Calabi-Yau manifolds of higher dimension, and the “mirror symmetry” which relates pairs of them. Various aspects of mirror symmetry have various mathematical implications, and we will explain how these are conjecturally related to each other.

    Codes MSC :
    14J32 - Calabi-Yau manifolds
    81T30 - String and superstring theories; other extended objects (e.g., branes)
    14J33 - Mirror symmetry

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 03/05/2016
      Date de captation : 15/04/2016
      Collection : Research schools ; Algebraic and Complex Geometry ; Mathematical Physics
      Format : MP4
      Durée : 01:58:36
      Domaine : Algebraic & Complex Geometry ; Mathematical Physics
      Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-04-15_morrison_part2.mp4

    Informations sur la rencontre

    Nom de la rencontre : School on the Mathematics of String Theory / Ecole sur les mathématiques de la théorie des cordes
    Organisateurs de la rencontre : Cheng, Miranda C. N. ; Kashani-Poor, Amir-Kian ; Minasian, Ruben ; Morrison, David R.
    Dates : 11/04/2016 - 15/04/2016
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1413.html

    Citation Data

    DOI : 10.24350/CIRM.V.18960303
    Cite this video as: Morrison, David R. (2016). Calabi-Yau manifolds, mirror symmetry, and $F$-theory - part II. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18960303
    URI : http://dx.doi.org/10.24350/CIRM.V.18960303


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