Weyl Law for 1-Cycles and Applications

This lecture explores the asymptotic behavior of volumes of minimal submanifolds in Riemannian manifolds, focusing on Gromov's conjecture from the 1980s. Discover how these volumes relate to the eigenvalues of the Laplacian operator, following a pattern similar to the Weyl Law for the Volume Spectrum. Learn about recent progress on this mathematical conjecture, with particular emphasis on the case of 1-cycles and their applications to generic density and equidistribution of stationary geodesic networks. The 58-minute presentation by Bruno Staffa at the Hausdorff Center for Mathematics delves into Almgren-Pitts Min-Max Theory and the Morse Theory of the volume functional in n-dimensional Riemannian manifolds.