Systolic and Diastolic Geometry - Eigenvalues and Minimal Surfaces

Explore a 51-minute lecture on "Eigenvalues and minimal surfaces" presented by Mikhail Karpukhin from University College London (UCL) as part of the "Systolic and Diastolic Geometry" event at IMPA (Instituto de Matemática Pura e Aplicada) in Rio de Janeiro. The lecture delves into the relationship between geometric analysis and minimal surfaces, examining how eigenvalue problems connect to fundamental questions in differential geometry. This presentation was part of a broader conference that brought together specialists studying comparison problems between volume of spaces and length/area of curves/surfaces, including topics like periodic orbits in billiards, geodesics on spheres, and Laplacian eigenvalues on surfaces. The event featured numerous international speakers addressing various aspects of systolic and diastolic geometry, aiming to advance research through innovative techniques that bridge geometric analysis and symplectic geometry.