Mathematical Sciences: Applications of Radon Transforms and Symplectic Geometry

小行星9626880 这个项目涉及对称空间上的调和分析和Radon变换。特别是，研究人员计划研究那些辛结构出现在超平面空间的Radon变换。几何概率论和克罗夫顿的积分公式也被认为是因为它们涉及到氡变换。 Radon变换背后的思想是重建几何对象-例如，空间中的凸体-从其截面数据或切片。由于其在计算机断层扫描和医学扫描设备中的应用，该领域最近受到了极大的关注。

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.