MATH-476 / 5 credits

Teacher:

Language: English

Remark: Pas donné en 2023-24


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.

Content

Learning Prerequisites

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.

Resources

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Optimal transport
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Optimal transport
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Optimal transport
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
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     

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