Aula Tonelli (SNS).
In this talk I will present the DynamicalMonge-Kantorovich model, a PDE system coupling an ellipticequation with a diffusion coefficient that change in timeaccording to a non-linear dynamics. The steady state of this system has been related to thedifferent Optimal Transport problems, offering an efficientnumerical scheme for their solution. We will explore someexamples of application, like identification of theCut-Locus of a point on manifold and the study of complexnatural network. The simplicity of the model allows simple but effectivetransformations of its core equations, that have been shownto be connected with different optimization problems,such as the Basis Pursuit Problem and the ShapeOptimization Problem.