Now showing items 1-10 of 22
The Group Structure on an Elliptic Curve
Quantum Field Theory for Homological Algebraists
The BV formalism in quantum field theory provides a homological theory of integration that can be used to compute path integrals. The present note is an overview of such ideas. Starting with a discussion of the combinatorial ...
Fiberedness of almost-Montesinos knots
In this paper we begin to classify fiberedness of "Almost-Montesinos" knots, a generalization of Montesinos knots. We employ the method used in the classification of fiberedness of Montesinos knots due to Hirasawa and ...
Developing scalable quartet tree encodings
Reconstructing the Tree of Life, the evolutionary history of all species, stands as one of the most significant and intensive problems in computational biology. One approach to this grand project is to use supertree ...
On L-functions and the Selberg class
The purpose of this thesis will be to explore the relationship between elliptic curves and L-functions. We will start o with a section giving some necessary defi nitions that will be used throughout the entire paper. ...
Global coordinate systems: Continuously moving finite-dimensional unit norm tight frames on smooth manifolds
Continuously moving bases for tangent spaces of manifolds are important in the study of differential geometry and mathematical physics. However, globally continuous bases do not exist for the tangent spaces of all manifolds, ...
Contact network epidemiology: Mathematical methods of modeling a mutating pathogen on a two-type network
With the threat of diseases like Sudden Acute Respiratory Syndrome (SARS) and Avian Flu that can lead to global pandemics, it is important to be able to understand how diseases spread through a population and predict how ...
When is a graph knotted?
Knot theory, as traditionally studied, asks whether or not a loop of string is knotted. That is, can we deform the loop in question into a circle without cutting or breaking it. In this thesis, I take a less traditional ...
Photonic topological insulators: Building topological states of matter
The discovery of topological insulators -- materials which are conventional insulators in the bulk but support dissipationless, "topologically protected" edge states -- has revolutionized condensed matter physics in recent ...
On the optimal stopping of Brownian motion
In this thesis, first we briefly outline the general theory surrounding optimal stopping problems with respect primarily to Brownian motion and other continuous-time stochastic processes. In Chapter 1, we provide motivation ...