Yevgeny Liokumovich (Massachusetts Institute of Technology)

Title: Weyl law for the volume spectrum

Abstract: To each cohomology class of the space of codimension 1 cycles, Min-Max theory associates a minimal hypersurface with some integer multiplicity. Volumes of these minimal hypersurfaces are called "widths" or "volume spectrum" of the manifold. Gromov conjectured that like eigenvalues of the Laplacian, the volume spectrum has asymptotic behaviour described by a Weyl law. I will discuss the proof of this conjecture, related open questions and directions. This is a joint work with Fernando Coda Marques and Andre Neves.