Teaching

Optimal Transport

This course is an introduction to the field of Optimal Transport. It aims at presenting central results in the field along with a few selected topics. The course is offered as an elective course in several Master and PhD programs at HSE University in both the Computer Science and Mathematics Faculty. Prerequisites for the course include a basic knowledge of Differential Calculus, Convex analysis, Measure Theory and Topology.

Lectures:

• Lecture 1. The optimal transport problem (January 21, 28) pdf
• Lecture 2. Existence of optimal transport plans (February 4) pdf
• Lecture 3. Kantorovich-Wasserstein distances (February 11) pdf
• Lecture 4. Necessary and sufficient optimality conditions (February 25) pdf
• Lecture 5. Duality and existence of optimal transport maps (March 4) pdf

References for the course:

• Lectures on Optimal Transport. Ambrosio L., Brué E. and Semola D.
• Statistical Optimal Transport. Chewi S., Niles-Weed J. and Rigollet P.
• Задачи Монжа и Канторовича оптимальной транспортировки. Богачев В.И., Колесников А. В., Шапошников С. В. (in Russian)
• A user’s guide to optimal transport. Ambrosio L. and Gigli N.
• Optimal Transport: Old and New. C. Villani.
• Topics in Optimal Transportation. C. Villani.
• Optimal Transport for Applied Mathematicians. P. Santambrogio.
• Computational Optimal Transport With Applications to Data Science. Peyré G. and Cuturi M.