Theoretical and numerical study of sharp isoperimetric inequalities

par Ilias Ftouhi (Nîmes)

lundi 23 mars 2026, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

In this talk, we introduce the notion of Blaschke–Santaló diagrams, which provide an effective framework for visualizing the sharpest inequalities relating given shape functionals. We present theoretical results concerning the analysis of such diagrams and discuss numerical methods developed for their approximation. Particular attention is devoted to diagrams involving both PDE-related functionals, such as the first eigenvalue of the Dirichlet Laplacian, and purely geometric quantities, including the volume and the perimeter. The presentation is based on joint works with Jimmy Lamboley (ENS Paris) and Eloi Martinet (University of Würzburg).