Autour des diagrammes de Blaschke--Santaló

Blaschke–Santaló diagrams visualize optimal inequalities connecting specified functionals. This talk introduces their underlying principles and main analytical methods through a detailed theoretical study of the diagram relating perimeter, volume and the first eigenvalue of the Dirichlet Laplacian. It then considers numerical methods for approximating such diagrams. The presentation draws on joint work with Jimmy Lamboley and Eloi Martinet.