Inverse problems for the connection Laplacian

Dr. Lauri Oksanen (University College London)

Frank Adams 2,

We reconstruct a Riemannian manifold and a Hermitian vector bundle with compatible connection from the hyperbolic Dirichlet-to-Neumann operator associated with the wave equation of the connection Laplacian. The boundary data is local and the reconstruction is up to the natural gauge transformations of the problem. As a corollary we derive an elliptic analogue of the main result which solves a Calderon problem for connections on a cylinder. The talk is based on joint work with Yaroslav Kurylev (University College London) and Gabriel P. Paternain (University of Cambridge).

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