Seminario EDPs y Mecánica de Fluidos

A uniqueness result for the Calderón problem for U(N)-connections coupled to Spinors

Ponente:  Carlos Valero (McGill University)
Fecha:  jueves 26 de mayo de 2022 - 12:00
Lugar:  Aula Naranja, ICMAT


We introduce the Dirichlet-to-Neumann (DN) map for the Dirac Laplacian coupled to a U(N)-connection A on a spin manifold with boundary, and show that it is a pseudodifferential operator of order 1 whose symbol determines the metric and connection to infinite order at the boundary. We go on to show that A can be recovered up to local gauge equivalence from the DN map in the real analytic category if it satisfies a Yang-Mills-Dirac equation in the interior; moreover, if N = 1, we can recover A up to global gauge equivalence.