RESUMEN: On compact Riemannian manifolds with boundary, the (anisotropic) Calderón’s problem asks to what extent the Dirichlet-to-Neumann map associated with the Laplace—Beltrami equation determines the metric (up to a natural obstruction). In this talk, I will discuss a similar problem, known as inverse scattering for asymptotically hyperbolic manifolds (i.e., manifolds that, outside a compact region, behave like the hyperbolic space): fixed an «energy level», and  given the analog of the Neumann data for solutions to certain 0-elliptic PDE depending on the fixed energy level, determine the metric of the manifold. I will show that, under some geometric conditions, one can determine the Taylor series of the metric at the boundary. The proof is based on the relation between this problem and the Calderón problem for the Conformal Laplacian.

LUGAR: Sala de Seminarios Felipe Alvarez Daziano, 5to PISO, Departamento de Ingeniería Matemática, FCFM Universidad de Chile.

MODALIDAD: Presencial y transmisión por Zoom. Link aquí: ZOOM