Calderon problem for connections

Mihajlo Cekic (University of Cambridge)

Frank Adams 2,

We will consider the problem of identifying a unitary connection \nabla on a vector bundle, up to gauge equivalence, from the Dirichlet-to-Neumann map of the connection Laplacian \nabla^*\nabla. One possible approach we will take is through the construction of special Complex Geometric Optics solutions and a further reduction of the problem to an X-ray transform. Alternatively, we will briefly consider another approach based on unique continuation property of elliptic equations (work in progress).

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