Optimal Transport and Applications.

A.Y. 2025/2026
6
Max ECTS
42
Overall hours
SSD
MAT/05
Language
Italian
Learning objectives
The course aims to provide students with an introduction to the theory of Optimal Transport. This theory is a very versatile tool that has found applications in recent years in many different areas of mathematics and its applications.
Expected learning outcomes
Learning of the basic notions and techniques in the theory of optimal transport and its applications.
Single course

This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.

Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
The course will be divided into 3 parts.
I. The Euclidean Optimal Transport Problem, the Discrete Case and the Kantorovich Formulation.
II. Solution to the Monge Problem with the Quadratic Cost.
III. Applications to PDEs and Calculus of Variations and the Wasserstein Space.
Prerequisites for admission
Basics in Real analisys.
Teaching methods
Lectures on blackboard.
Teaching Resources
F. Maggi, Optimal Mass Transport on Euclidean Spaces, Cambridge studies in advanced mathematics, 207.
Assessment methods and Criteria
The exam consists of a written test. During the written test you will be asked to illustrate some results (and proofs) of the teaching program, as well as to solve some exercises, in order to evaluate your knowledge and understanding of the topics covered, as well as your ability to apply them.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Lessons: 42 hours
Professor: Cavalletti Fabio
Professor(s)