Nonlinear Geometry of Banach Spaces and Metric Spaces

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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.