Dr. Gunther Uhlmann
Department of Mathematics
Title: 30 years of Calderón's inverse problem
Abstract: Caldern's problem consists in finding the electrical conductivity of a medium by making voltages and current measurements at the boundary. In mathematical terms one tries to determine the coefficient of a partial differential equation by measuring the corresponding Dirichlet-to-Neumann map. This problem arises in geophysical prospection and it has been proposed as a diagnostic tool in medical imaging, particular early breast cancer detection. We will also describe the progress that has been made on this problem since Calderón's seminal paper in 1980.
Prior to the seminar, please join Dr. Uhlmann and the Department of Mathematics for coffee in Weber 117 at 3:30 pm.
Title: Travel Time Tomography and Boundary Rigidity
Abstract: In this lecture we will describe a surprising connection between Caldern's inverse problem and travel time tomography. This latter problem consists in determining the index of refraction (sound speed) of a medium by measuring the travel times of sound waves going though the medium. In mathematical terms the question is to determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between points on the boundary. In differential geometry this is known as the boundary rigidity problem. This inverse problem arises in geophysics in determining the inner structure of the Earth by measuring the travel times of seismic waves as well as in ultrasound imaging.
Prior to the seminar, please join Dr. Uhlmann and the Department of Mathematics for coffee in Weber 117 at 10:30am.
Title: Cloaking, Invisibility and Inverse Problems
Abstract: We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves, acoustic waves and quantum waves. For the case of electromagnetic waves, Maxwell's equations have transformation laws that allow for design of electromagnetic materials that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. The object, which would have no shadow, is said to be cloaked. We recount the recent history of the subject and discuss some of the mathematical issues involved.
Please join Dr. Uhlmann at a reception following his lecture in 117 Weber.
The lectures are supported by the Arne Magnus Lecture Fund and the Albert C. Yates Endowment in Mathematics.
Contributions to the Magnus Fund are greatly appreciated and may be made through the Department of Mathematics. Please contact Sheri Hofeling (firstname.lastname@example.org) at at (970)-491-7047 for specific information.
All lectures are free and open to the public.