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This lecture presents "Vector Valued Optimal Transport: From Dynamic to Kantorovich Formulations" by Katy Craig from the University of California, Santa Barbara, recorded on April 29, 2025, at IPAM's Dynamics of Density Operators Workshop. Explore a unified theory connecting four existing notions of vector valued optimal transport, motivated by applications in multispecies PDE and classification of vector valued measures. Learn about the sharp inequality that proves these notions are bi-Holder equivalent, and examine the comparative properties of each metric from gradient flows and linearization perspectives. The 52-minute presentation offers valuable insights for researchers and students interested in optimal transport theory and its applications. Access additional resources through IPAM's workshop page at UCLA.
