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Fall 2023
The aim of this thesis is to provide an exposition to Mochizuki and Hoshi's approach to birational anabelian geometry of mixed characteristic local fields. In the introductory chapter, we begin by recalling the relevant backgrounds on the Grothendieck conjectures on the étale fundamental groups...
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Characterizing Population Heterogeneity of Salmonella Motion in Mucosal Environments Using Stochastic Modeling and the EM Algorithm
DownloadFall 2022
Salmonella are pathogenic bacteria that infect many species including humans. This pathogen thrives in the gastrointestinal track of their hosts and propel themselves in mucus with motion structures called flagella. Each cell has multiple flagella that can rotate either synchronously, resulting...
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Fall 2020
The kinetic chemotaxis equations have long been used to model biological processes. We will analyze a volume filling variant of the kinetic chemotaxis equations on the torus. Since the kinetic chemotaxis systems have well known blow-up solutions, we spend a considerable amount of time showing...
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Spring 2019
Let $G$ be a linear algebraic group defined over a ground field $k$, and let $\mu$ be a $\Gal(k^\sep/k)$-module.A \tb{cohomological invariant} is a morphism $a:H^1(-,G)\to H^n(-,\mu)$ of two functors from the category of field extensions over $k$ to the category of setswhere $H^1(-,G)$ is the...
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Spring 2019
Atkin and Swinnerton-Dyer conjectured a simple characterization of those Fuchsian groups whose modular forms have integral Fourier coefficient. It has a natural and far-reaching generalization, which we will call the vASD conjecture, to vector-valued modular forms. We confirm vASD conjecture for...
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Fall 2018
In this thesis, we explore the relationship between graphical representations of the 1-dimensional N-extended supersymmetry algebra called Adinkras, compact Riemann surfaces, and quivers. An Adinkra is a graph which was originated in physics to study off-shell representations of the supersymmetry...
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Fall 2016
Ferrofluids are liquids with a magnetic colloid suspended by Brownian motion which become magnetized in the presence of an external magnetic field. They have recently garnered a lot of interest due to their wide range of applications in industry and biomedicine. For example, ferrofluids are used...
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Fall 2013
This thesis considers PVol (Percentage of Volume) strategies, which are an often used type of algorithmic trading strategies. In a PVol strategy, the broker aims to bring the order execution speed in line with a percentage of the market volume. This target percentage and the total order size are...
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Spring 2011
This thesis pursues the study of non-algebraic and non-Kahler compact complex manifolds by traditionally algebraic methods involving sheaves, cohomology and K-theory. To that end, Bott-Chern cohomology is developed to complement De Rham and Dolbeault cohomology. The first substantial chapter is...