Optimal Transport

Part I. Short Courses: 1. Introduction to optimal transport theory Filippo Santambroggio; 2. Models and applications of optimal transport in economics, traffic and urban planning Filippo Santambroggio; 3. Logarithmic Sobolev inequality for diffusions and curvature-dimension condition Ivan Gentil; 4. Lecture notes on variational methods for incompressible Euler equations Luigi Ambrosio and Alessio Figalli; 5. Ricci flow: the foundations via optimal transportation Peter Topping; 6. Lecture notes on gradient flows and optimal transport Sara Danieri and Guiseppe Savare; 7. Ricci curvature, entropy, and optimal transport Shin-Ichi Ohta; Part II. Survey and Research Papers: 8. Computing the time-continuous optimal mass transport without Lagrangian techniques Olivier Besson, Martine Picq and Jerome Poussin; 9. On the duality theory for the Monge-Kantorovich transport problem Mathias Beiglbock, Chrsitian Leonard and Walter Schachermayer; 10. Optimal coupling for mean field limits Francois Bolley; 11. Functional inequalities via Lyapunov conditions Patrick Cattiaux and Arnaud Guillin; 12. Size of the medial axis and stability of Federer's curvature measures Quentin Merigot.