Calderon problem for connections

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• Mihajlo Cekic (Cambridge)
• Friday 04 March 2016, 15:00-16:00
• MR13.

If you have a question about this talk, please contact Christian Lund.

We consider the problem of determining the connection on a vector bundle from the knowledge of the associated Dirichlet-to-Neumann map. This problem admits a natural gauge symmetry, namely automorphisms fixing the boundary. In this talk we will discuss the approach based on Limiting Carleman Weights, that allow us to construct the Complex Geometric Optics solutions (CGO). We will shortly describe how to construct the CGOs from the Gaussian Beams, which are approximate eigenfunctions of the Laplacian that concentrate along geodesics. A reconstruction procedure will be discussed in the case of line bundles and also the interaction between the unique continuation principle and the holonomy with the Cauchy data.

This talk is part of the Junior Geometry Seminar series.

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