Recorded 29 April 2025. Katy Craig of the University of California, Santa Barbara, presents "Vector Valued Optimal Transport: From Dynamic to Kantorovich Formulations" at IPAM's Dynamics of Density Operators Workshop. Abstract: Motivated by applications in multispecies PDE and classification of vector valued measures, we develop a unified theory that connects four existing notions of vector valued optimal transport. We prove a sharp inequality relating the four notions, showing they are bi-Holder equivalent, and compare and contrast the properties of each metric from the perspective of gradients flows and linearization. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-dynamics-of-density-operators/