MS 08: Linear and non-linear tomography in non Euclidean geometries

Tue, 28 March, 2017, 16:30–18:30, Room: UC 202DH

Organizers

Plamen Stefanov, Francois Monard, and Gunther Uhlmann

Abstract

In media with a metric, or more generally, a connection, the X-ray transform over geodesics appears as the linearization of the non-linear inverse problem known as travel-time tomography: in the metric case, can one reconstruct the metric from the scattering relation: endpoints and directions of geodesics with given initial points and directions; and the corresponding travel times. In seismology, this is related to recovery of the structure of the Earth from travel times of seimic waves measured at the surface. This problem has a natural extension to connections: reconstructing a connection from knowledge of its parallel transport along geodesics. In these non-linear problem as well as their linear counterpart, unique identifiability, stability and explicit inversions are inferred, and the answer to these questions strongly depends on the underlying geometry (in particular, the presence of caustics and/or trapping). This minisymposium aims at bringing the experts in this field to communicate their most recent progress.

List of speakers

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