During the last two decades deep results have been obtained regarding the mathematical theory of Optimal Transport problems, with striking applications in wide mathematical areas: calculus of variations, analysis of Partial Differential Equations (in particular Monge-Ampere, nonlinear diffusion, Fokker-Planck, transport equations), first order mean-field games, geometric and functional inequalities, non-smooth analysis in metric-measure spaces, Riemannian geometry, probability.
On the basis of this impressive theoretical apparatus, new promising research directions have more recently emerged, mainly focused on various challenging models and problems arising from applications: we quote here control of crowd and congested motions, image processing, big data and machine learning, and economics. In all these rapidly evolving areas, the general and unifying approach of Optimal Transport has been combined with specific problems and techniques: new algorithms and powerful computational strategies have been developed, allowing for new and quite efficient numerical methods.
The school aims to give a broad overview on these recent progresses with a series of lectures given by some of the leading experts in this ﬁeld.
The school is mainly addressed to Ph.D. students, advanced master students and postdocs.