Multi angle

H 1 A Polyakov formula for sectors

Auteurs : Rowlett, Julie (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Polyakov’s formula expresses a difference of zeta-regularized determinants of Laplace operators, an anomaly of global quantities, in terms of simple local quantities. Such a formula is well known in the case of closed surfaces (Osgood, Philips, & Sarnak 1988) and surfaces with smooth boundary (Alvarez 1983). Due to the abstract nature of the definition of the zeta-regularized determinant of the Laplacian, it is typically impossible to compute an explicit formula. Nonetheless, Kokotov (genus one Kokotov & Klochko 2007, arbitrary genus Kokotov 2013) demonstrated such a formula for polyhedral surfaces ! I will discuss joint work with Clara Aldana concerning the zeta regularized determinant of the Laplacian on Euclidean domains with corners. We determine a Polyakov formula which expresses the dependence of the determinant on the opening angle at a corner. Our ultimate goal is to determine an explicit formula, in the spirit of Kokotov’s results, for the determinant on polygonal domains.

    Codes MSC :
    58C40 - Spectral theory; eigenvalue problems
    58J52 - Determinants and determinant bundles, analytic torsion
    35K08 - Heat kernel

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 12/05/2016
      Date de captation : 28/04/2016
      Collection : Research talks ; Partial Differential Equations ; Geometry ; Mathematical Physics
      Format : MP4
      Durée : 00:47:07
      Domaine : PDE ; Geometry ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-04-28_Rowlett.mp4

    Informations sur la rencontre

    Nom de la rencontre : Evolution equations on singular spaces / Équations d'évolution sur les espaces singuliers
    Organisateurs de la rencontre : Baskin, Dean ; Hillairet, Luc ; Wunsch, Jared
    Dates : 25/04/2016 - 29/04/2016
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1396.html

    Citation Data

    DOI : 10.24350/CIRM.V.18964603
    Cite this video as: Rowlett, Julie (2016). A Polyakov formula for sectors. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18964603
    URI : http://dx.doi.org/10.24350/CIRM.V.18964603

    Voir aussi


    1. Aldana, C.L., & Rowlett, J. (2015). A Polyakov formula for sectors. - http://arxiv.org/abs/1411.7894

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