Gunther Uhlmann

Abstract: Inverse problems arise in all fields of science and technology where causes for a desired or observed effect are to be determined. By solving an inverse problem is in fact is how we obtain a large part of our information about the world. An example is human vision: from the measurements of scattered light that reaches our retinas, our brains construct a detailed three-dimensional map of the world around us. We know about the interior structure of the Earth by using the information provided by earthquakes, the structure of DNA from solving inverse X-ray diffraction problems, and the structure of the atom and its constituents from studying the scattering when materials are bombarded with particles. Medical imaging is also a fertile area of application of inverse problems including CT scans, ultrasound, MRI, and several other imaging methods.

We will concentrate in this talk on the Mathematics of travel time tomography: can we determine the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium? This can be recast as geometry problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? No previous knowledge of inverse problems or differential geometry will be assumed.

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Ivan Losev.