Mathematical aspects of information geometry

  • Jürgen Jost (Max Planck Institute for Mathematics in the Sciences, Germany)
University n.n. Universität Leipzig (Leipzig)


In this talk, I shall explore the connections of information geometry with various mathematical fields. The Fisher metric is seen as the natural metric on an infinite dimensional projective space. This also yields a geometric interpretation of Green functions (propagators) of quantum field theory. In finite dimensional situations, the Fisher metric induces a pair of dual affine structures. Such a geometry is called K\"ahler affine or Hessian. I shall define a natural differential operator associated to such a structure, the affine Laplacian, and discuss an existence theorem for affine harmonic mappings.

02.08.10 06.08.10

Information Geometry and its Applications III

Universität Leipzig (Leipzig) University n.n. University n.n.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences, Germany

Paolo Gibilisco

Università degli Studi di Roma "Tor Vergata", Italy

František Matúš

Academy of Sciences of the Czech Republic, Czech Republic