Explore a cutting-edge seminar on optimal transport of matrix-valued measures presented by renowned mathematician Yann Brenier from École Normale Supérieure, Paris. Delve into a novel approach for defining optimal transport of positive-semidefinite matrix-valued measures, inspired by recent developments in rendering incompressible Euler equations and related conservative systems as concave maximization problems. Discover the main outcome of this research: a matricial analogue of the Hellinger-Kantorovich metric spaces. Gain valuable insights into advanced mathematical concepts and their applications in the field of partial differential equations during this hour-long presentation hosted by the Society for Industrial and Applied Mathematics.