The Calderón problem for U(N)-connections coupled to spinors

Carlos Valero, McGill University

The Calderón problem refers to the question of whether one can determine the Riemannian metric on a manifold with boundary from its "Dirichlet-to-Neumann (DN) map", which maps a function on the boundary to the normal derivative of its harmonic extension. In this talk, we define the analogue of the DN map for the spinor Laplacian twisted by a unitary connection and show that it is a pseudodifferential operator of order 1, whose symbol determines the Taylor series of the metric and connection at the boundary. We go on to show that if all the data are real-analytic, then the spinor DN map determines the connection modulo gauge.

MC 5417