This dissertation presents some new results in certain areas of structural graph theory. In particular we are concerned with graph minors, and classes of graphs characterised in part by forbidding certain minors. There are ...

In this paper it is established that there is a faithful functor E from the category T whose objects are locally finite classical trees of minimal vertex degree three and whose morphisms are classes of quasi-isometries to ...

We construct a uniform version of the analytic K-homology theory and prove its basic properties such as a Mayer-Vietoris sequence. We show that uniform K-homology is isomorphic to a direct limit of K-theories of certain ...

We extend the list of known diagram groups which satisfy a conjecture of Guba and Sapir. Specifically, Guba and Sapir extended the notion of the Stallings foldings for free groups to diagram groups, and showed that given ...

In the main part of this dissertation we present a method for finding the critical probability for the Bernoulli bond percolation and the critical inverse temperature for Ising model on graphs with the so-called tree-like ...

We study the interplay between spectral morphisms, K-theory, and stable ranks for Banach algebras and, more generally, for Frechet algebras with open group of invertibles. After some preliminaries on the Gelfand transform, ...

This thesis summarizes the research I have done during my graduate tenure at Vanderbilt University. The core of the thesis is a model of glueballs as tightly knotted or linked chromoelectric flux tubes. The model is based ...