Geometry and Topology Seminar

The p-widths of a closed Riemannian manifold are a nonlinear analogue of the spectrum of its Laplace--Beltrami operator, which was defined by Gromov in the 1980s and corresponds to areas of a certain min-max sequence of hypersurfaces. By a recent theorem of Liokumovich--Marques--Neves, the p-widths obey a Weyl law, just like the eigenvalues do. However, even though eigenvalues are explicitly computable for many manifolds, there had previously not been any >=
2-dimensional manifold for which all the p-widths are known. In recent joint work with Otis Chodosh, we found all p-widths on the round 2-sphere and thus the previously unknown Liokumovich--Marques--Neves Weyl law constant in dimension 2.