Andrew Swift Thesis Defense: On some problems in nonlinear Banach space geometry

Date: April 24, 2018

Time: 11:00AM - 12:00PM

Location: BLOC 220

Speaker: Andrew Swift

Description: Two general problems in the nonlinear geometry of Banach spaces are to determine the relationship between uniform and coarse embeddability and to characterize local/asymptotic properties in terms of metric structure. The purpose of this research is to investigate these problems and to contribute to a better overall understanding of the structure of Banach spaces and metric spaces. We use general techniques found in the literature to study three specific examples. First, we investigate the relationship between the small-scale and large-scale structures of $c_0(\kappa)$. Next, we investigate the relationship between the small-scale and large-scale structures of superstable Banach spaces. Finally, we define a vertex-labeling for a class of graphs we call the ``bundle graphs'', and use this to generalize some known characterizations of Banach space properties in terms of graph preclusion.