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Colloquium

Wed., Feb. 3, 2016 3:30 p.m.

Location: CL 431

  • Speaker:  Asghar Ghorbanpour
  • Title: Noncommutative Geometry and the Spectral Action Principle 
  • Abstract: Noncommutative geometry is a rapidly developing field with extensive applications in the other fields of modern mathematics as well as  physics.
    In this new paradigm of geometry, proposed by Fields Medalist  Alain Connes,  the geometric objects are so called spectral triples (A, H, D).
    In this setting, the topological information are encoded in the C*-algebra A and the geometric information, are encoded in the spectrum of the self adjoint operator  D
    (with compact resolvent) and these two are related by their representation on the Hilbert space H}.
    To be able to model physical theories on these spaces, the spectral action principle was introduced by A. Connes and A. Chamseddine. We will start by a brief review of the  principle and  describe techniques that can be employed to calculate the asymptotic expansion of the spectral action.
    In particular, I will recall Connes and Chamseddine's calculation of the spectral action for Robertson-Walker metrics and the rationality of their spectral action that we proved in the joint work with M. Khalkhali and F. Fathizadeh [JHEP12(2014)064].