Spectra of non-linear opeartors

Eigenvalues of the Laplace operator capture important geometric features of the underlying Riemannian manifold, or a graph or whatever space on which one can fancy to define the operator.

Some other geometrically important invariants, such as Cheeger constant, systoles, Gromov's/Guth's widths appear as "eigenvalues" of some non-linear operators, sometimes defined on non-linear functional spaces.

I will discuss some ways to make rigorous definition of a spectrum of non-linear operator and natural questions (such as stability of the spectrum) that appear along the way.