Seminar talk, 16 March 2022

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Speaker: Dmitri Alekseevsky

Title: Special Vinberg cones and their applications

The talk is based on joint works with Vicete Cortes, Andrea Spiro and Alessio Marrani.

A short survey of the Vinberg theory of convex cones (including its informational geometric interpretation) and homogeneous convex cones will be presented. Then we concentrate on the theory of rank 3 special Vinberg cones, associated to metric Clifford modules.

A generalization of the theory to the indefinite special Vinberg cones, associated to indefinite metric Clifford modules is indicated. An application of special Vinberg cones to Supergravity will be considered.

We will discuss also applications of theory of homogeneous convex cones to convex programming, information geometry and Frobenius manifolds.