Speaker: Baha Alzalg (Ohio State University and the University of Jordan)
Title: The algebraic properties of Einstein-Minkowski causality cone and its extensions.
Abstract: In this talk, we present the algebraic properties of the nonconvex second-order cone (SOC), which is a nonconvex conic extension of the known convex SOC in mathematics and operations research, as well as a higher dimen-sional conic extension of the known causality cone in relativity. The cone can arise in real-world applications such as the facility location problem. We give the dual cone of the nonconvex SOC in both the Euclidean and pseudo-Riemannian spaces. We also define notions of its algebraic structure, and find that this algebraic structure is a commutative power-associative magma whose elements always have real eigenvalues; this is remarkable because it is not the case for arbitrary Jordan algebras. We will also see that the magma of this nonconvex cone is rankly independent of its dimension; this is also remarkable because it is not the case for algebras of arbitrary convex cones. Even more remarkably, we prove that the nonconvex SOC equals the cone of squares of its magma; this is not the case for all non-Euclidean Jordan algebras. In addition, numerous algebraic properties that already exist in the framework of the convex SOC are generalized to the framework of the nonconvex SOC.
Zoom: https://osu.zoom.us/j/99598622548?pwd=cG1kczJPZVpmd29KeFFYOVFEZHlGdz09