Optimal Transport and Applications.
A.Y. 2026/2027
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
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.
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
At the student's discretion, the exam will consist either of a seminar on a topic agreed upon with the professor or of a written examination, which will include an exercise and a theoretical section. For the theoretical section, all definitions and statements of the results presented in class may be the subject of questions, as well as a selection of the corresponding proofs.
MATH-03/A - Mathematical Analysis - University credits: 6
Lessons: 42 hours
Professor:
Cavalletti Fabio
Shifts:
Turno
Professor:
Cavalletti FabioProfessor(s)