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.

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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.

In 1889, Josef Stefan proposed a model for how ice melts---seemingly simple, yet so mathematically stubborn that it took 134 years to prove that the surface of melting ice stays smooth. This talk will unravel the solution to this problem in its simplest form: the obstacle problem, a cornerstone of free boundary problems. We'll use this classic example to introduce the fascinating world of free boundary problems, where the unknowns include not just the solution, but the very domain in which the equations hold. These problems arise naturally in physics (melting, fluid dynamics), but also in finance (optimal stopping), biology, and beyond. Expect a gentle dive into the methodology and approaches used to tackle partial differential equations (PDEs), with a focus on intuition, visual examples, and the beauty of connecting abstract math to real-world phenomena.