9626880 Smirnov This project deals with harmonic analysis on symmetric spaces and Radon transforms. In particular, the investigator plans to study those symplectic structures appearing as Radon transforms on the space of hyperplanes. Geometric probability theory and Crofton's integral formula are also to be considered as they relate to Radon transforms. The idea behind Radon transforms is to reconstruct a geometric object - e.g., a convex body in space - from its sectional data or slices. This field has received a great deal of attention recently due to its applications in computerized tomography and medical scanning devices.
