SMS scnews item created by Daniel Daners at Thu 22 Mar 2018 0950
Type: Seminar
Modified: Thu 22 Mar 2018 2051; Mon 26 Mar 2018 0916
Distribution: World
Expiry: 26 Mar 2018
Calendar1: 26 Mar 2018 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: PDE Seminar: Journey to the Center of the Earth (Uhlmann)

PDE Seminar

Journey to the Center of the Earth


Gunther Uhlmann
University of Washington, USA
Mon 26th Mar 2018, 2-3pm, Carslaw Room 829 (AGR)

Update: Those interested in joining lunch please meet at 12:00 at the Taste Baguette in the Law School Annex.


We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.

We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

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Enquiries to Daniel Hauer or Daniel Daners.

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