25 jan 2023 -- 14:30
Aula Seminari, DISMA, Politecnico di Torino
Differential Geometry Seminar Torino
Abstract.
We shortly review the Hessian Riemannian geometry of convex cones and their Vinberg’s description as cones of positive definite Hermitian matrices in the generalized matrix algebra (Vinberg T-algebra). We indicate the statistical interpretation of such cones and discuss different applications of the Vinberg theory. We discuss the problem of classifying homogeneous convex cones and give a description of special Vinberg cones of rank 2 and 3 associated to graded Clifford modules. We describe the r-map, which associates to a special Vinberg cone a homogeneous special Kaehler manifold, and c-map, associated to a homogeneous special or quaternionic Kaehler manifold. We also give a physical interpretation of these maps. At the end, we discuss the application of special Vinberg cones for computing the entropy of BPS static black holes in N=2, D=4 Supergravity.
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