Filippo Santambrogio (Université Claude Bernard - Lyon 1)
Introduction to Optimal Transport and Applications
(Introduzione al Trasporto Ottimale e Applicazioni)

(12 hours)

Online PhD course


Teams code:

Please contact prof. Porretta
( for information, or for being added to the Teams channel

Tentative program:
  • Monge and Kantorovich problems, existence of optimal plans, dual problem, and existence of Kantorovich potentials.
  • Strong duality (inf sup = sup inf). Existence of optimal maps, the quadratic case, and the Monge-Ampère equation. Application to the isoperimetric inequality.
  • Optimal transport for the distance cost. Wasserstein distances, curves in the Wasserstein spaces and the continuity equation.
  • Geodesics in the Wasserstein spaces. The Benamou-Brenier method for numerical computations. Geodesically convex functionals.
  • Introduction to gradient flows in metric spaces; the JKO minimization scheme for some parabolic equation. Heat and Fokker-Planck equations as gradient flows in the Wasserstein space (convergence of the scheme).

Scheduled lectures:

May 17  h 11-13
May 19  h 16.30-18.30
May 20  h 11.30-13.30
May 24  h 11-13
May 26  h 16.30-18.30
May 27  h 11.30-13.30