Le séminaire des doctorants se propose de fournir aux doctorants une occasion de s'ouvrir aux autres domaines des mathématiques que le leur. A chaque séance, un intervenant réalise un exposé sur un fait standard de leur domaine d'étude, de niveau adapté à l'ensemble des doctorants.

---

Optimal transport is an active research area with strong connections with partial differential equations and with functional inequalities arising in analysis and probability, as well as to applied fields including economics, machine learning, and image processing.
To better address the needs arising from these applications, several extensions of the classical optimal transport framework have been introduced over the years. In this presentation, I will discuss some of these related problems.
I will begin by introducing entropic optimal transport, a regularized version of optimal transport that is particularly well suited for numerical computation and large-scale applications. I will then present unbalanced optimal transport, which allows for mass variation and is especially relevant in machine learning contexts. Finally, I will discuss multi-marginal optimal transport, a generalization of the classical two-marginal problem.
For each of these extensions, I will outline the main motivations, key theoretical properties, and representative applications.

The PhD students seminar aims to provide PhD students with an opportunity to explore other areas of mathematics beyond their own. At each session, a speaker gives a presentation on a standard topic in their field of study, at a level suitable for all doctoral students.