MATS423 Optimal Mass Transportation (5 cr)
Description
Monge and Kantorovitch formulations of optimal mass transportation, existence and uniqueness of optimal transport maps, Wasserstein distance, and brief introduction to functionals on Wasserstein spaces. Optionally applications of optimal mass transportation.
Learning outcomes
The student is able to formulate the optimal mass transportation problem and prove the existence of its solution under suitable assumptions.
Description of prerequisites
Measure and integration theory 1 and 2
The courses Functional analysis, Real analysis and Advanced measure theory will be useful but not mandatory.
Study materials
lecture notes
L. Ambrosio and N. Gigli: A user's guide to optimal transport http://cvgmt.sns.it/paper/195/
A. Figalli and F. Glaudo, An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
C. Villani, Optimal Transportation - Old and New https://cedricvillani.org/sites/dev/files/old_images/2012/08/preprint-1.pdf
Literature
- L. Ambrosio , E. Brué , D. Semola, Lectures on Optimal Transport, ISBN: 978-3-030-72161-9
Completion methods
Method 1
Method 2
Participation in teaching (5 cr)
lectures and exercises