Mathematical Sciences: Banach Spaces and Convexity Theory

女性研究机会奖支持沃纳教授在Banach空间理论方面的工作。她的项目的一个部分涉及Banach空间的性质，这些性质可以通过适当的重排的存在来刻画，例如，包含同构于绝对可和序列空间的子空间的性质。她还将研究欧几里得空间中凸体的几何。Banach空间的理论是关于无限多个维度的分析。对于每个有限维n，只有一个n维空间，在大多数方面，就像在n为1、2或3的常见情况下一般被理解的那样。这些空间用于跟踪只有有限多个自由度的情况。当自由度数变得无限时，例如描述一段弦的构型将是必要的，对于在其中执行分析的环境空间有许多可能的合理选择。将这些空间区分开来的一个关键结构元素是距离的测量方式。沃纳教授的项目关注的是以某种方式重新调整距离测量的能力如何影响空间的几何结构。

This Research Opportunities for Women award supports Professor Werner's work in Banach space theory. One part of her project concerns properties of Banach spaces that can be characterized by the existence of appropriate renormings, for instance the property of containing a subspace isomorphic to the space of absolutely summable sequences. She will also investigate the geometry of convex bodies in Euclidean space. The theory of Banach spaces is about analysis in infinitely many dimensions. For each finite dimension n, there is only one n-dimensional space, in most respects as well understood in general as in the familiar cases when n is 1, 2, or 3. These are used to keep track of situations in which there are only finitely many degrees of freedom. When the number of degrees of freedom becomes infinite, as would for instance be necessary to describe the configuration of a piece of string, there are many possible reasonable choices for the ambient space in which to perform analysis. A key element of structure that distinguishes these spaces one from another is the way in which distance is measured. Professor Werner's project is concerned with how the ability to rescale the distance measurement in certain ways impinges on the geometrical structure of the space.