MATH-476 / 5 crédits

Enseignant: Colombo Maria

Langue: Anglais

## Summary

The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functional/geometric inequalities, traffic models.

## Required courses

Basic background in analysis (Analysis i-iV, measure theory and metric spaces)

## Recommended courses

A few concepts of functional analysis (briefly reviewed along the course).

## Learning Outcomes

By the end of the course, the student must be able to:

• Describe the fundamental concepts about Optimal transport, such as the duality theory and the structure of optimal maps
• Solve exercises and master meaningful examples
• Explore and present recent research papers on the topic
• Identify connections between the optimal transport theory and other mathematical problems (such as in PDEs, functional inequalities)

## Assessment methods

Oral exam. Exercises presented orally and specific homeworks give a bonus of up to 1.

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Optimal transport
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Optimal transport
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Optimal transport
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22