Workshop Analyse Harmonique - WAH !

    Organisers

• Michael Pevzner
• Rupert Yu

    Partners

• Fédération de recherche ARC (Amiens-Reims-Compiègne) Mathématiques FR 3399
• Bonus Qualité Recherche (BQR) de l'Université de Reims Champagne-Ardenne
  Programme Spécial « Groupes et Représentations » Reims 2012

    Participants

    Talks (45 minutes)

• S. Gindikin (Rutgers, USA)
  Horospheric geometry of symmetric spaces. (2 talks)
  The fundamental project of Gelfand to develop harmonic analysis on symmetric spaces on the base of the horospherical duality was for a long time realized only for a relatively narrow class of symetric spaces. I believe that the union of this approach with complex geometrical analysis makes it universal.
  
• T. Kobayashi (Tokyo, Japon)
  Global Geometry and Analysis on Locally Homogeneous Spaces. (2 talks)
  The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure. Further, almost nothing is known on global analysis on such spaces. Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:
  1. (global shape) Is a locally homogeneous space closed?
  2. (spectral analysis) Does spectrum of the Laplacian vary when we deform the geometric structure?
  
• V. Molchanov (Tambov, Russie)
  Complex hulls of the hyperboloid of one sheet and the analytic continuation of spherical functions. (2 talks)
  For the hyperboloid of one sheet in \({\Bbb R}^3\), we construct four complex hulls and continue analytically to them spherical functions of different series (continuous (twice), holomorphic and antiholomorphic). For any of these series, we write the projection operator and the Cauchy-Szegö kernel.

    Programme