Conférence donnée dans le cadre de la procédure d’appel en mathématiques, Professor Position in Mathematics.

Summary: One of the most fundamental and important questions in Partial Differential Equations (PDE) is that of regularity. It stands as a unifying problem in the field since it affects all kinds of PDEs, ranging from Hilbert's XIXth problem, to fully nonlinear PDE, free boundary problems, integro-differential operators, optimal transport, minimal surfaces, geometric flows, etc.
In this talk, I will give an overview of part of my research related to regularity issues for elliptic PDE. In doing so, I will introduce the notions of integro-differential operators, as well as the most classical free boundary problem: the obstacle problem.