Mathematical Sciences: Banach Space Theory and Convexity Theory

9401784 Werner教授建议继续她在巴拿赫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面体近似的联系。在巴拿赫空间理论中，她计划继续研究与Radon Nikodym性质有关的问题。一个固体被称为凸，如果一个线段连接它的两个点停留在体内。凸体通常可以被描述为良好凸集（如半平面）的交点。这里考虑的一个问题是，一个凸体是否可以很好地近似于只有有限个顶点的凸体。当逼近物体的体积接近原物体的体积或者它们的表面积接近时，这个近似就是好的。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. ***