## Speaker:

Christos Mantoulidis

Rice University

## Time:

Tuesday, May 17, 2022 - 4:00pm

## Location:

ISEB 1200

Abstract: 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.