Outline

  1. Basic definitions: homogeneous convex cones and the dual cones.
  2. Applications of homogeneous convex cones
  3. Homogeneous convex cones as Riemannian manifolds
  4. Köcher-Vinberg classification of selfdual homogeneous convex cones.
  5. Rank 3 Special Vinberg cones.
  6. Special Kähler and spacial quaterniionic Kähler manifolds associated to a special Vinberg cone. Physical interpretation.
  7. Application of the Vinberg cones to Supergravity. Calculation of Beken-stein-Hawking entropy of a BPS static black hole in N=2 D=4 Supergravity.

The talk is based on a joint works with Vicente Cort´es (Transformation Groups, 2020) and Alessio Marrani and Andrea Spiro (J. Higher Energy Phy-sics, 2021) .

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