Mathematical Sciences: Non-linear Aspects of the Geometry ofConvex Sets

首席研究员将继续研究 凸集几何学 该项目将集中在某些 非线性几何问题 一个长期目标是扩大 研究人员和其他人的各种已知结果， 复杂的格拉斯曼人 这些问题的动机是 几何的，经常与积分几何有联系 和随机几何学 Radon理论中的技术 将使用变换、球谐函数和分布 在这项新的研究中。 像球、立方体和金字塔这样的固体是 凸集 这样的人从不向内鞠躬。 交叉口 两个这样的集合总是凸的，而它们的并集往往不是。 在更高的维度中，类似集合特别重要， 业务应用。 在这个项目中，研究人员将 将凸集理论的思想扩展到更广泛的领域， 几何设置。

The principal investigator will continue his research into the geometry of convex sets. The project will focus on certain non-linear geometric problems. A long-term goal is to extend various known results by the investigator and others to more complex Grassmannians. The motivation for these problems is geometrical and frequently has connections with integral geometry and stochastic geometry. Techniques from the theory of Radon transforms, spherical harmonics, and distributions will be used in this new study. Solids such as the ball, cube, and pyramid are examples of convex sets. Such sets never bow inward. The intersection of two such sets is always convex, while their union, often not. Analogous sets in higher dimensions are particularly important in business applications. In this project the investigator will extend ideas from the theory of convex sets to a wider range of geometric settings.