The question at the heart of Optimal Transport is: How does one define the cost of moving one distribution of mass (pile of sand, population, particles,…) in order to cover another (hole to fill, destinations,…), but doing so with the least amount of effort? Although the actual definition of such a cost ends up quite simple and arguably intuitive (it still took 160 years for L. Kantorovich to bring a rigorous answer, after the first formulation by G. Monge in 1781…), the strength of Optimal Transport lies in the large variety of situations that it can model. This versatility has allowed it to make an appearance and bring powerful tools to many mathematical fields, from partial differential equations, to statistical analysis and machine learning.
In this course, the goal will be to gradually introduce the type of optimization problems that are usually seen in optimal transport. We will start from the discrete, combinatoric cases (this part will require very little knowledge past basic linear algebra and topology), and generalize to more general point distributions. We will then mention a few of its contributions to other scientific fields, in order to give a first glimpse into the many applications of this very fruitful topic.
Mon. 13:30-15:30, room M
Tue. 10:30-12:30, meeting room, 2nd floor CV2
Wed. 10:30-13:30, meeting room, 2nd floor CV2
Thu. 15:30-18:30, meeting room, CV1 entrance hall
Fri. 11:30-13:30, room F