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H 1 Formal conjugacy growth and hyperbolicity

Auteurs : Ciobanu, Laura (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Rivin conjectured that the conjugacy growth series of a hyperbolic group is rational if and only if the group is virtually cyclic. In this talk I will present the proof (joint with Hermiller, Holt and Rees) that the conjugacy growth series of a virtually cyclic group is rational, and then also confirm the other direction of the conjecture, by showing that the conjugacy growth series of a non-elementary hyperbolic group is transcendental (joint with Antolín). The result for non-elementary hyperbolic groups can be used to prove a formal language version of Rivin's conjecture for any finitely generated acylindrically hyperbolic group G, namely that no set of minimal length conjugacy representatives of G can be regular.

    Codes MSC :
    20F67 - Hyperbolic groups and nonpositively curved groups
    68Q45 - Formal languages and automata

      Informations sur la Vidéo

      Réalisateur : Vichi, Pascal
      Langue : Anglais
      Date de publication : 13/10/15
      Date de captation : 17/09/15
      Collection : Research talks ; Algebra ; Computer Science
      Format : MP4 ; audio/x-aac
      Durée : 00:48:56
      Domaine : Algebra ; Computer Science
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-09-17_Ciobanu.mp4

    Informations sur la rencontre

    Nom de la rencontre : GAGTA-9: Geometric, Asymptotic and Combinatorial Group Theory and Applications / GAGTA-9 : Théorie géométrique, asymptotique et combinatoire des groupes et applications
    Organisateurs de la rencontre : Coulbois, Thierry ; Weil, Pascal
    Dates : 14/09/15 - 18/09/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1212.html

    Citation Data

    DOI : 10.24350/CIRM.V.18836803
    Cite this video as: Ciobanu, Laura (2015). Formal conjugacy growth and hyperbolicity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18836803
    URI : http://dx.doi.org/10.24350/CIRM.V.18836803


    1. Antolín, Y., & Ciobanu, L. (2015). Formal conjugacy growth in acylindrically hyperbolic groups. - http://arxiv.org/abs/1508.06229

    2. Ciobanu, L., Hermiller, S., Holt, D., & Rees, S. (2014). Conjugacy languages in groups. - http://arxiv.org/abs/1401.7203