Nonlinear Geometry of Banach Spaces and Metric Spaces

主要研究者将调查问题的功能分析，特别是对几何的Banach和度量空间。该建议保持其重点的渐近版本的里贝计划。PI对一般度量空间感兴趣，并试图确定在特定映射集下闭合的Banach空间类。PI已经做了一些有趣的工作，并期望从这个项目中得到更多。这些构成了该提案的智力价值。该项目中处理的主题涉及分析的许多领域和分析之外的领域，包括算子理论，群论，几何分析和理论计算机科学，这些构成了该提案更广泛影响的一部分。此外，首席研究员是各种委员会的成员，其目标是与本科生进行对话或帮助改善他们的学习条件。

The principal investigator will investigate problems in functional analysis, specifically on the geometry of Banach and metric spaces. The proposal keeps its focus on the asymptotic version of the Ribe program. The PI is interested in general metric spaces and seeks to identify classes of Banach spaces that are closed under specific sets of maps. The PI has done some interesting work and much more is expected from this project. These constitute the intellectual merit of the proposal.The topics treated in this project make contact with many areas of analysis and areas outside of analysis, including operator theory, group theory, geometric analysis, and theoretical computer science, and these constitute part of the broader impacts of the proposal. Furthermore, the principal investigator is a member of various committees who goals is to either create a dialogue with undergraduate students or help improve their learning condition.