Kantorovich Duality and Optimal Transport Problems on Magnetic Graphs

Abstract

We consider Lipschitz- and Arens-Eells-type function spaces constructed for magnetic graphs, which are adapted to the magnetic setting from the classical area of optimal transport on discrete spaces. After establishing the duality between this spaces, we prove a characterization of the extreme points of the unit ball in the (magnetic) Lipschitz space as well as a semi-constructive result relating the (magnetic) Arens-Eells norm for functions defined on a magnetic graph to the (classical) Arens-Eells norm for functions defined on the so-called magnetic lift graph.Biography: Sawyer Jack Robertson is interested in mathematical analysis who has engaged in research activities out of the OU math department for two years. He is a two-time consecutive recipient of OU Libraries’ Undergraduate Research award. His 2019 paper describes a connection between two spaces which help model transport phenomena, and is currently working to extend this result to more general areas.University Libraries Undergraduate Research Award