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H 1 Computing Hecke operators for cohomology of arithmetic subgroups of $SL_n(Z)$

Auteurs : McConnell, Mark W. (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We will describe two projects. The first which is joint with Avner Ash and Paul Gunnells, concerns arithmetic subgroups $\Gamma$ of $G = SL_4(Z)$. We compute the cohomology of $\Gamma \setminus G/K$, focusing on the cuspidal degree $H^5$. We compute a range of Hecke operators on this cohomology. We fi Galois representations that appear to be attached to the Hecke eigenclasses, based on the operators we have computed. We have done this for both non-torsion and torsion classes. The second project, which is joint with Bob MacPherson, is an algorithm for computing the Hecke operators on the cohomology $H^d$ of $\Gamma$ in $SL_n(Z)$ for all $n$ and all $d$.

    Keywords : automorphic forms; cohomology of arithmetic groups; Hecke operators; Galois representations

    Codes MSC :
    11F60 - Hecke-Petersson operators, differential operators (several variables)
    11F75 - Cohomology of arithmetic groups
    11F80 - Galois representations
    20J06 - Cohomology of finite groups

    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/1995/Slides/mcconnell_slides.pdf

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 17/04/2019
      Date de captation : 25/03/2019
      Collection : Research talks ; Number Theory
      Format : MP4
      Durée : 01:02:50
      Domaine : Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-03-25_Mcconnel.mp4

    Informations sur la rencontre

    Nom de la rencontre : Cohomology of arithmetic groups, lattices and number theory: geometric and computational viewpoint / Cohomologie des groupes arithmétiques, réseaux et théorie des nombres: géométries et calculs
    Organisateurs de la rencontre : Bayer-Fluckiger, Eva ; Elbaz-Vincent, Philippe ; Ellis, Graham ; Gunnels, Paul
    Dates : 25/03/2019 - 29/03/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1995.html

    Citation Data

    DOI : 10.24350/CIRM.V.19508903
    Cite this video as: McConnell, Mark W. (2019). Computing Hecke operators for cohomology of arithmetic subgroups of $SL_n(Z)$. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19508903
    URI : http://dx.doi.org/10.24350/CIRM.V.19508903


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