Mathematical Sciences: Applications of Radon Transforms and Symplectic Geometry

9626880斯米尔诺夫这个项目研究对称空间上的调和分析和Radon变换。特别是，研究人员计划研究超平面空间上出现的Radon变换的辛结构。几何概率论和Crofton积分公式也要考虑，因为它们与Radon变换有关。Radon变换背后的想法是根据截面数据或切片重建几何对象--例如，空间中的凸体。近年来，由于其在计算机层析成像和医学扫描设备中的应用，该领域受到了极大的关注。

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.