The talk will review a new approach to the limits of the quantum N-body dynamics leading to the Hartree equation (in the large N limit) and to the Liouville equation (in the small Planck constant limit). This new strategy for studying both limits involves functionals that are analogous to the Wasserstein distance of exponent 2 used in optimal transport. (Work in collaboration with Clément Mouhot and Thierry Paul).
