Bell, Gregory

uncg

There are 7 item/s.

TitleDateViewsBrief Description
An obstruction to property A 2018 290 We discuss large scale geometric properties of Cayley graphs of the integers using different infinite generating sets. We define the notion of k-prisms for graphs and study the large scale geometry of graphs with this property. It turns out that grap...
On characterizing pairs of permutations in determining their generated group 2013 2483 Among the unsolved problems in mathematics listed on Wolfram Mathworld's website is finding a formula for the probability that two permutations chosen at random generate the symmetric group. We show that two permutations of order two cannot generate ...
Multi-scale persistent homology 2016 1209 Data has shape and that shape is important. This is the anthem of Topological Data Analysis (TDA) as often stated by Gunnar Carlsson. In this paper we take a common method of persistence involving the growing of balls of the same size, and generalizi...
Multiradial (multi)filtrations and persistent homology 2016 1016 Motivated by the problem of optimizing sensor network covers, we generalize the persistent homology of simplicial complexes over a single radial parameter to the context of multiple radial parameters. The persistent homology of so-called multiradial ...
Asymptotic dimension and asymptotic property 2011 2137 This thesis will be concerned with the study of some ``large-scale'' properties of metric spaces. This area evolved from the study of geometric group theory. Chapter 1 lays out some of the fundamental notions of geometric g...
Permanence results for dimension-theoretic coarse notions 2014 838 Coarse topology is the study of interesting topological properties of discrete spaces. In this dissertation, we will discuss a coarse analog of dimension and several generalizations. We begin by extending the class of metric spaces for which these pr...
On the preservation of coarse properties over products and on persistence curves 2019 478 We explore two facets of topology, coarse and computational, that share a similar philosophy: “The perceived shape of a space depends on the scale at which that space is viewed”. In coarse topology, we analyze the preservation of properties of coarse...