Theses and Dissertations  Department of Mathematics
Recent Submissions

Hodge and Gelfand theory in Clifford analysis and tomography
There is an interesting inverse boundary value problem for Riemannian manifolds called the Calderón problem which asks if it is possible to determine a manifold and metric from the DirichlettoNeumann (DN) operator. Work ... 
Nonlinear dynamics of plant pigmentation
Red, blue, and purple colors in plants are primarily due to plant pigments called anthocyanins. In a plant cell, an equilibrium is established between anionic and cationic forms of anthocyanins as well electrically neutral ... 
Imprimitively generated designs
Designs are a type of combinatorial object which uniformly cover all pairs in a base set V with subsets of V known as blocks. One important class of designs are those generated by a permutation group G acting on V and ... 
Full waveform inversion for ultrasound computed tomography in the deterministic and Bayesian settings
Ultrasound computed tomography (USCT) is a noninvasive imaging technique in which acoustic waves are sent through a region and measured after transmission and reflection in order to provide information concerning that ... 
Determining synchronization of certain classes of primitive groups of affine type
The class of permutation groups includes 2homogeneous groups, synchronizing groups, and primitive groups. Moreover, 2homogeneous implies synchronizing, and synchronizing in turn implies primitivity. A complete classification ... 
Molecular configurations and persistence: branched alkanes and additive energies
Energy landscapes are highdimensional functions that encapsulate how certain molecular properties affect the energy of a molecule. Chemists use disconnectivity graphs to find transition paths, the lowest amount of energy ... 
Resource allocation for space domain awareness and synthetic aperture radar
In this thesis, we will address two resource allocation problems. For each of these problems, the objective will be to make use of the resources in an optimal way. We will consider the Space Domain Awareness (SDA) sensor ... 
Quantum Serre duality for quasimaps
Let X be a smooth variety or orbifold and let Z ⊆ X be a complete intersection defined by a section of a vector bundle E → X. Originally proposed by Givental, quantum Serre duality refers to a precise relationship between ... 
Weighted ensemble: practical variance reduction techniques
Computational biology and chemistry is proliferated with important constants that are desirable for researchers. The meanfirstpassage time (MFPT) is one such important quantity of interest and is pursued in molecular ... 
Stability in the weighted ensemble method
In molecular dynamics, a quantity of interest is the mean first passage time, or average transition time, for a molecule to transition from a region A to a different region B. Often, significant potential barriers exist ... 
Symmetric functions, shifted tableaux, and a class of distinct Schur Qfunctions
The Schur Qfunctions form a basis of the algebra Ω of symmetric functions generated by the odddegree power sum basis pd, and have ramifications in the projective representations of the symmetric group. So, as with ordinary ... 
Modular group and modular forms
We prove some results about the structure of SL2(Z) and related groups. We define modular forms for this group and develop the basic theory. We then use the theory of lattices to construct examples of modular forms. 
Some topics in combinatorial phylogenetics
This thesis is in combinatorial phylogenetics and is focused on a study of Hadamard conjugation. It examines the question of whether the presence of an abelian permutation group acting regularly on the states is necessary ... 
Arithmetic in group extensions using a partial automation
The purpose of this paper is to describe the structure of an extension group G which has a normal subgroup K and a quotient group Q = G/K . To describe the structure of G concretely, we want to be able to do arithmetic in ... 
Iterative matrix completion and topic modeling using matrix and tensor factorizations
With the everincreasing access to data, one of the greatest challenges that remains is how to make sense out of this abundance of information. In this dissertation, we propose three techniques that take into account ... 
Independence complexes of finite groups
Understanding generating sets for finite groups has been explored previously via the generating graph of a group, where vertices are group elements and edges are given by pairs of group elements that generate the group. ... 
Analysis of domain decomposition methods using deal.II, An
Iterative solvers have attracted significant attention since the mid20th century as the computational problems of interest have grown to a size beyond which direct methods are viable. Projection methods, and the two ... 
Classifying simplicial dissections of convex polyhedra with symmetry
A convex polyhedron is the convex hull of a finite set ofpoints in R3. A triangulation of a convex polyhedron is a decomposition into a finite number of 3simplices such that any two intersect in a common face or are ... 
Moduli spaces of rational graphically stable curves
We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a ... 
Generalizations of persistent homology
Persistent homology typically starts with a filtered chain complex and produces an invariant called the persistence diagram. This invariant summarizes where holes are born and die in the filtration. In the traditional ...