Title: Wonderful mathematics of tomography

 

Abstract:

Tomography (seeing the interior of a non-transparent body) has become ubiquitous, with main applications in medicine (those amazing CT, MRI, ultrasound, and quite a few other scanners), as well as in geophysics, seismology, oil prospection, astronomy, industrial non-destructive testing, homeland security, and even archeology. For a mathematician, though, the main attraction is the beautiful, hard, and diverse mathematical problems it leads to. Practically anything from "pure" mathematics (well, I do not believe the partition into pure and applied math) gets involved: PDEs, geometry (differential, integral, algebraic), harmonic analysis (classical and abstract), discrete mathematics, certainly numerical analysis, and more or less anything else one can imagine. This is why a huge and growing community of mathematicians enjoy this Eden.

 

In the talk I will try to convey some of this beauty. Although the presentation is directed to mathematicians, no prior knowledge of tomography will be assumed.

 

Bio: Peter Kuchment is a University Distinguished Professor of Mathematics at Texas A&M University. His research interests include partial differential equations, mathematical physics, and integral geometry and their applications. He has made seminal contributions in the areas such as computed tomography, quantum graphs, differential equations, and photonic crystals, for which he was elected a Fellow of the Institute of Physics, American Mathematical Society, American Association for the Advancement of Science, Society for Industrial and Applied Mathematics, and the American Physical Society. He is also a Senior Member of the Institute of Electrical and Electronics Engineers (2015).

He is the author of over 200 papers and books and has delivered numerous lectures and lecture series around the world. Kuchment is also interested in enhancement of K-12 education: he is the founding director of the SMaRT summer math camp, has co-founded Texas A&M's Math Fest, and co-directed a correspondence math program for middle- and high school students at the Wichita State University in Kansas.

Kuchment received his Ph.D. in Mathematics from Kharkov University (Ukraine) in 1973 and his Doctor of Science degree from the Mathematics Institute of the Academy of Sciences of Ukraine in 1983.