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H 1 Covering spaces and spanning trees

Auteurs : Cimasoni, David (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The aim of this talk is to show how basic notions traditionally used in the study of "knotted embeddings in dimensions $3$ and $4$", such as covering spaces and representation theory, can have non-trivial applications in combinatorics and statistical mechanics. For example, we will show that for any finite covering $G'$ of a finite edge-weighted graph $G$, the spanning tree partition function on $G$ divides the spanning tree partition function on $G'$ (in the polynomial ring with variables given by the weights). Setting all the weights equal to $1$, this implies a theorem known since 30 years: the number of spanning trees on $G$ divides the number of spanning trees on $G'$. Other examples of such results will be presented.
    Joint work (in progress) with Adrien Kassel.

    Codes MSC :
    05C30 - Enumeration in graph theory
    57M12 - Special coverings
    82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 18/02/2018
      Date de captation : 15/02/2018
      Collection : Research talks ; Geometry ; Topology
      Format : MP4
      Durée : 01:02:31
      Domaine : Topology ; Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-02-15_Cimasoni.mp4

    Informations sur la rencontre

    Nom de la rencontre : Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4
    Organisateurs de la rencontre : Audoux, Benjamin ; Baader, Sebastian ; Lecuona, Ana G.
    Dates : 12/02/2018 - 16/02/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1893.html

    Citation Data

    DOI : 10.24350/CIRM.V.19357503
    Cite this video as: Cimasoni, David (2018). Covering spaces and spanning trees. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19357503
    URI : http://dx.doi.org/10.24350/CIRM.V.19357503


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