Fall 2009, Thursdays, Milner 216, 4:00-4:50 PM

Date: September 10

"  Tomography - mathematics of seeing invisible "
  Prof. Peter Kuchment  


I will present a brief introduction to the so called Tomography, which is a technology that enables one to see inside of a non-transparent body. Many of you have heard about CAT and MRI tomographic scanners currently available in most hospitals. Tomography is extremely useful in all kinds of applications, e.g. in medical diagnostics (search for tumors), non-destructive evaluation in industry (checking for interior cracks in materials), oil and water prospecting, deep Earth geophysics imaging, and border inspection. The crucial thing is that there is no "film" involved, like in the case of X-ray pictures, and the final high images result from intricate MATHEMATICAL procedures. The mathematics of tomography is extremely beautiful and diverse. It involves manifold techniques that are of general importance for mathematicians (either pure or applied), engineers, physicists, and other scientists. Among these one can mention Fourier Analysis, Differential and Integral Geometry, Complex Analysis, Differential Equations, Numerical Methods, and what not. New tomographic methods that require new mathematical solutions are being constantly developed (in particular at the mathematics, biomedical engineering, and nuclear engineering departments at TAMU).

Time permitting (which is unlikely), I might touch upon other topics of my interest.