Outline
- Basic definitions: homogeneous convex cones and the dual cones.
- Applications of homogeneous convex cones
- Homogeneous convex cones as Riemannian manifolds
- Köcher-Vinberg classification of selfdual homogeneous convex cones.
- Rank 3 Special Vinberg cones.
- Special Kähler and spacial quaterniionic Kähler manifolds associated to a special Vinberg cone. Physical interpretation.
- 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) .
