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

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


Plamen Stefanov, Francois Monard, and Gunther Uhlmann


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

Gabriel Paternain
Effective inversion of the attenuated X-ray transform associated with a connection
Marco Mazzucchelli
On Marked boundary rigidity for surfaces
Lauri Oksanen
The light ray transform and applications
Hanming Zhou
Generic uniqueness and stability of inverse problems for connections
Sean Holman
Exploring generic conditions for stability of the geodesic ray transform