Jueves 11 de agosto 14.30. Aula 27
Título: «Inverse spectral results for the Dirichlet-to-Neumann operator»
Resumen; The Dirichlet-to-Neumann operator of a compact Riemannian manifold M with boundary is a linear map $C^\infty(\partial M)\to C^\infty(\partial M)$ that maps the Dirichlet boundary values of each harmonic function f on M to the Neumann boundary values of f. The spectrum of this operator is discrete and is called the Steklov spectrum. The Dirichlet-to-Neumann operator also generalizes to the setting of orbifolds. We will compare the behavior of the Steklov spectrum on smooth surfaces with that of two-dimensional orbifolds. If time permits, we will also discuss the adaptation to the Steklov setting of techniques for constructing isospectral manifolds.