Mathematical Sciences: Banach Space Theory and Convexity Theory

9401784 Werner教授建议继续她在Banach空间理论和凸性理论方面的研究。在凸性理论中，她想进一步研究凸体的漂浮体和照明体的性质，以及它们与仿射表面积和凸体的多边形逼近的关系。在Banach空间理论方面，她计划继续研究与Radon Nikodym财产有关的问题。如果连接实体两点的线段位于实体内，则实体称为凸体。凸体通常可以描述为精细凸集的交集，如半平面。这里考虑的问题之一是，凸体是否可以很好地用只有有限个顶点的凸体来近似。在近似体的体积接近于原始体的体积的意义上，或者从它们的表面积接近的意义上说，近似是好的。第二个项目涉及应用于概率论的抽象数学。***

9401784 Werner Professor Werner proposes to continue her research in Banach space theory and convexity theory. In convexity theory she wants to investigate further properties of floating and illumination bodies of convex bodies as well as their connection with affine surface area and approximation of convex bodies by polytopes. In Banach space theory she plans to continue her work on problems related to the Radon Nikodym property. A solid body is called convex in case a line segment joining two of its points stays within the body. Convex bodies can frequently be described as intersections of nice convex sets such as half-planes. One of the questions considered here is whether a convex body can be nicely approximated by convex bodies having only a finite number of vertices. The approximation is to be good in the sense that volumes of the approximating bodies are close to the volume of the original body or in the sense that their surface areas are close. The second project involves abstract mathematics that has applications to probability theory. ***