Introduction to Optimal Transport and Applications
(Introduzione al Trasporto Ottimale e Applicazioni)
(12 hours)


Online PhD course

Link: https://teams.microsoft.com/l/channel/19%3a13403b0057ec4b5fae5f0acefcebc5fb%40thread.tacv2/Generale?groupId=2a674b5f-4484-43a0-94fc-804a6dcdf8b2&tenantId=24c5be2a-d764-40c5-9975-82d08ae47d0e

Teams code: 9dd7am8

Please contact prof. Porretta (porretta@mat.uniroma2.it) 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