Title | Date | Views | Brief Description |
Asymptotic dimension and asymptotic property |
2011 |
2046 |
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 |
2186 |
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 ... |
Permanence results for dimension-theoretic coarse notions |
2014 |
755 |
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... |
Multi-scale persistent homology |
2016 |
1066 |
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 |
836 |
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 ... |
An obstruction to property A |
2018 |
236 |
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 the preservation of coarse properties over products and on persistence curves |
2019 |
350 |
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... |