Travel Time Tomography, Boundary Rigidity, and Tensor Tomography

Travel Time Tomography is the inverse problem in which one attempts to determine the parameters of a medium by measuring the travel time of waves going through the medium. One of the potential applications is the determination of the inner structure of the earth by measuring the travel times of seismic waves using seismograms located in many places in the world.

The Boundary Rigidity Problem consists in the determination of a Riemannian metric of a compact Riemannian manifold with boundary by measuring the boundary distance function between boundary points. The Riemannian metric models the anisotropic index of a refraction of the medium. The boundary distance function measures the first arrival times of waves. Tensor Tomography is the linearized problem. This consists in the determination of a symmetric tensor fields from its integral along geodesics. It also arises in other applications like photoelasticity.

From January, 2007 to April 2007, some of the world experts in these subjects will be in residence at UW, including Nurlan Dairbekov (Kazakh British Technical University, Kazakhstan), Plamen Stefanov (Purdue University), and Vladimir Sharafutdinov (Sobolev Institute of Mathematics, Russia). These researchers, Gunther Uhlmann and his graduate students will give introductory and research seminars on the subject.

Lectures:

Regular Day: Monday
Regular Time: 2:30pm
Regular Place: Padelford C-36

· January 29

Nurlan Dairbekov, Boundary rigidity problem in the presence of a magnetic field

· February 5

Nurlan Dairbekov, Cohomological equation for magnetic flows and its applications

· Wednesday, February 14, 3:50pm

Plamen Stefanov, Lens rigidity for a class of non-simple manifolds

· February 26

Vladimir Sharafutdinov, On the non-linear inverse problem of polarization tomography

· Wednesday, February 28, 3:50pm

Vladimir Sharafutdinov, Conformal killing symmetric tensor fields on a Riemannian manifold