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H 1 Isomorphisms between eigenspaces of slow and fast transfer operators

Auteurs : Pohl, Anke (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Over the last few years I developed (partly jointly with coauthors) dual 'slow/fast' transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for certain hyperbolic surfaces/orbifolds L \ H with cusps (both of finite and infinite area; arithmetic and non-arithmetic).
    Both types of transfer operators arise from discretizations of the geodesic flow on L \ H. The eigenfunctions with eigenvalue 1 of slow transfer operators characterize Maass cusp forms. Conjecturally, this characterization extends to more general automorphic functions as well as to residues at resonances. The Fredholm determinant of the fast transfer operators equals the Selberg zeta function, which yields that the zeros of the Selberg zeta function (among which are the resonances) are determined by the eigenfunctions with eigenvalue 1 of the fast transfer operators. It is a natural question how the eigenspaces of these two types of transfer operators are related to each other.

    Codes MSC :
    11F03 - Modular and automorphic functions
    37C30 - Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
    37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 23/03/17
      Date de captation : 15/03/17
      Collection : Research talks ; Partial Differential Equations ; Number Theory ; Mathematical Physics
      Format : MP4
      Durée : 00:58:05
      Domaine : PDE ; Number Theory ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-03-15_Pohl.mp4

    Informations sur la rencontre

    Nom de la rencontre : Resonances: geometric scattering and dynamics / Résonances : scattering géométrique et dynamique
    Organisateurs de la rencontre : Guillarmou, Colin ; Hilgert, Joachim ; Pasquale, Angela ; Przebinda, Tomasz
    Dates : 13/03/17 - 17/03/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1604.html

    Citation Data

    DOI : 10.24350/CIRM.V.19142903
    Cite this video as: Pohl, Anke (2017). Isomorphisms between eigenspaces of slow and fast transfer operators. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19142903
    URI : http://dx.doi.org/10.24350/CIRM.V.19142903

    Voir aussi


    1. Adam, A., & Pohl, A. (2016). Isomorphisms between eigenspaces of slow and fast transfer operators. - https://arxiv.org/abs/1606.09109

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