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H 1 Twisted equivariant $\mathrm{K}$-theory and topological phases

Auteurs : Kubota, Yosuke (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real $\mathrm{K}$-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner’s theorem, is introduced by Freed and Moore by using a generalization of twisted $\mathrm{K}$-theory. In this talk, we introduce the definition of twisted $\mathrm{K}$-theory in the sense of Freed-Moore for $C^*$-algebras, which gives a framework for the study of topological phases of non-periodic systems with a symmetry of quantum mechanics. Moreover, we introduce uses of basic tools in $\mathrm{K}$-theory of operator algebras such as inductions and the Green-Julg isomorphism for the study of topological phases.

    Codes MSC :
    46L85 - Noncommutative topology
    81R60 - Noncommutative geometry
    81V70 - Many-body theory; quantum Hall effect
    19L50 - Twisted K-theory; differential K-theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/05/16
      Date de captation : 19/04/16
      Collection : Research talks ; Mathematical Physics
      Format : MP4
      Durée : 00:53:08
      Domaine : Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-04-19_Kubota.mp4

    Informations sur la rencontre

    Nom de la rencontre : Spectral theory of novel materials / Théorie spectrales des nouveaux matériaux
    Organisateurs de la rencontre : Exner, Pavel ; Kotani, Motoko ; Kuchment, Peter ; Zagrebnov, Valentin A.
    Dates : 18/04/2016 - 22/04/2016
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1399.html

    Citation Data

    DOI : 10.24350/CIRM.V.18962503
    Cite this video as: Kubota, Yosuke (2016). Twisted equivariant $\mathrm{K}$-theory and topological phases. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18962503
    URI : http://dx.doi.org/10.24350/CIRM.V.18962503

    Voir aussi


    1. Kubota, Y. (2016). Controlled topological phases and bulk-edge correspondence. - http://arxiv.org/abs/1511.05314

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