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H 1 Nodal lines and domains for Eisenstein series on surfaces

Auteurs : Naud, Frédéric
CIRM (Editeur )

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    Résumé : Eisenstein series are the natural analog of ”plane waves” for hyperbolic manifolds of infinite volume. These non-$L^2$ eigenfunctions of the Laplacian parametrize the continuous spectrum. In this talk we will discuss the structure of nodal sets and domains for surfaces. Upper and lower bounds on the number of intersections of nodal lines with ”generic” real analytic curves will be given, together with similar bounds on the number of nodal domains inside the convex core. The results are based on equidistribution theorems for restriction of Eisenstein series to curves that bear some similarity with the so-called ”QER” results for compact manifolds.

    Codes MSC :
    35J05 - Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
    58J50 - Spectral problems; spectral geometry; scattering theory
    58J51 - Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 30/03/15
      Date de captation : 10/03/15
      Collection : Research talks ; Partial Differential Equations ; Dynamical Systems and Ordinary Differential Equations ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 00:47:59
      Domaine : PDE ; Dynamical Systems & ODE ; Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-03-10_Naud.mp4

    Informations sur la rencontre

    Nom de la rencontre : Analysis and geometry of resonances / Analyse et géométrie des résonances
    Organisateurs de la rencontre : Guillarmou, Colin ; Hilgert, Joachim ; Pasquale, Angela ; Przebinda, Tomasz
    Dates : 09/03/15 - 13/03/15
    Année de la rencontre : 2015
    URL Congrès : http://www.math.univ-metz.fr/~pasquale/C...

    Citation Data

    DOI : 10.24350/CIRM.V.18732603
    Cite this video as: Naud, Frédéric (2015). Nodal lines and domains for Eisenstein series on surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18732603
    URI : http://dx.doi.org/10.24350/CIRM.V.18732603


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