Systolic Inequalities for S1-Invariant Contact Forms

Watch this short talk by Simon Vialaret from Paris-Saclay University on "Systolic inequalities for S1-invariant contact forms" presented at the Systolic and Diastolic Geometry event held at IMPA (Instituto de Matemática Pura e Aplicada) in Rio de Janeiro. The 28-minute presentation explores geometric problems comparing volume of spaces with lengths/areas of curves/surfaces they contain. This talk was part of a larger conference examining fundamental questions in Geometric Analysis and Symplectic Geometry, including topics like periodic orbits in convex billiards, geodesics on spheres, and Laplacian eigenvalue problems. The event brought together specialists from different mathematical backgrounds to advance research through innovative techniques inspired by analogies between these related geometric problems.