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Gabriel Paternain works on the interaction between differential geometry, dynamical systems and inverse problems. His notes with Will J. Merry connect the geodesic flow and Anosov flows to the X-ray transform and boundary rigidity. The guiding reconstruction problem asks how much of an interior Riemannian metric can be determined from measurements of trajectories or distances at the boundary.^[ref]

By Will J. Merry, Gabriel P. Paternain.

Lecture notes.