Lectures on Optimal Transport
This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transpor...
| Main Authors: | , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2021, 2021
|
| Edition: | 1st ed. 2021 |
| Series: | La Matematica per il 3+2
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 1 Lecture 1: Preliminary notions and the Monge problem
- 2 Lecture 2: The Kantorovich problem
- 3 Lecture 3: The Kantorovich - Rubinstein duality
- 4 Lecture 4: Necessary and sufficient optimality conditions
- 5 Lecture 5: Existence of optimal maps and applications
- 6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport
- 7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds
- 8 Lecture 8: The metric side of Optimal Transport
- 9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport
- 10 Lecture 10: Wasserstein geodesics, nonbranching and curvature
- 11 Lecture 11: Gradient flows: an introduction
- 12 Lecture 12: Gradient flows: the Brézis-Komura theorem
- 13 Lecture 13: Examples of gradient flows in PDEs
- 14 Lecture 14: Gradient flows: the EDE and EDI formulations
- 15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space
- 16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup
- 17 Lecture 17: The Benamou-Brenier formula
- 18 Lecture 18: An introduction to Otto’s calculus
- 19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature