**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)

Auth: daners@dora.maths.usyd.edu.au

### PDE Seminar

# Journey to the Center of the Earth

### Uhlmann

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.

## Abstract

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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