# Seminar talk, 16 March 2022

Speaker: Dmitri Alekseevsky

Title: Special Vinberg cones and their applications

Abstract:
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 ${\displaystyle Cl({\mathbb {R} }^{n})}$ modules.

A generalization of the theory to the indefinite special Vinberg cones, associated to indefinite metric Clifford ${\displaystyle Cl({\mathbb {R} }^{p,q})}$ modules is indicated. An application of special Vinberg cones to ${\displaystyle N=2,\,d=5,4,3}$ Supergravity will be considered.

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

Video