Poly-Jacobi Geometry: a Serendipitous Discovery

Abstract: With motivations in the implementation of physical dimension into geometric mechanics, I will introduce the formalism of dimensioned algebra and the unit-free approach to Jacobi geometry. These will be shown to lead to a natural generalization of Jacobi/Poisson geometry where many constructions, such as products and quotients, become much more natural. Finally, I will present a breadth of structures, tentatively called Poly-Jacobi, which are natural to define within this formalism but don't seem to have been identified in the Poisson literature.

mathematical physicsalgebraic geometrydifferential geometrydynamical systemssymplectic geometry

Audience: researchers in the topic

Junior Global Poisson Workshop II