Mathematical Sciences: Banach Space Theory and Convexity Theory

小行星9401784 沃纳教授建议继续她在Banach空间理论和凸性理论的研究。在凸性理论，她想进一步研究性质的浮动和照明机构的凸机构，以及他们的联系与仿射表面积和近似凸机构的多面体。在巴拿赫空间理论，她计划继续她的工作有关的问题，氡Nikodym财产。 一个固体称为凸的情况下，线段连接其两个点停留在身体。凸体通常可以被描述为良好的凸集，如半平面的交集。这里考虑的问题之一是凸体是否可以很好地近似凸体只有有限数量的顶点。在近似物体的体积接近于原始物体的体积的意义上，或者在它们的表面积接近的意义上，近似是好的。第二个项目涉及抽象数学，有应用概率论。 ***

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. ***