Mathematical Sciences: Stability Properties of Geometric Inequalities

主要研究者将研究 几何不等式是积分几何和凸几何的一个分支。 特别是他将调查的稳定性对称化 程序和分析不等式，以及布伦- 闵可夫斯基理论 这些研究需要了解 椭球体和帽状体。 这个项目涉及数学的重叠， 几何学和概率论 一个典型的问题可能是 找出二维空间中任意一条直线 与给定的正方形或其他凸多边形相交。 解决 这些问题在作战行动中有各种各样的应用 研究和其他应用领域。 调查员将 继续他在更高维度上对类似问题的研究。

The principal investigator will study the stability of geometric inequalities, a branch of integral and convex geometry. In particular he will investigate the stability of symmetrization procedures and analytic inequalities, and duals of Brunn- Minkowski theory. These studies will require the understanding of ellipsoids and cap bodies. This project involves mathematics at the overlap between geometry and probability theory. A typical problem might be to find the probability that a random line in two dimensions intersects a given square or other convex polygon. Solutions to these problems have a variety of applications in Operations Research and other applied areas. This investigator will continue his studies of similar problems in higher dimension.