Date: Wednesday, April 11, 2018
Location: B844 East Hall (4:00 PM to 5:00 PM)
Title: Ziwet Lecture 2: Journey to the Center of the Earth
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 socalled lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the Xray 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.
Files:
Speaker: Gunther Uhlmann
Institution: University of Washington
Event Organizer: John Schotland
