Bell, Gregory

uncg

There are 5 item/s.

TitleDateViewsBrief Description
Asymptotic dimension and asymptotic property 2011 1775 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...
On characterizing pairs of permutations in determining their generated group 2013 1774 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 686 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 594 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 ...
On the preservation of coarse properties over products and on persistence curves 2019 6 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...