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Spring 2019

Taylor, Mitchell A.

Suppose $X$ is a vector lattice and there is a notion of convergence $x{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x\alpha-x\rvert \wedge u\xrightarrow{\sigma} 0$ for every...

Fall 2012

Davis, William L

Cholera remains epidemic and endemic in the world, causing thousands of deaths annually in locations lacking adequate sanitation and water infrastructure. Yet its dynamics are still not fully understood. An indirectly transmitted infectious disease model, called an iSIR model, was recently...

Fall 2011

Gong, Jiafen

Cancer is one of the major causes of death in the world. In the field of Oncology, clinical trials form the crux of medical effort to find better treatment schedules. These trials are expensive, time consuming, and carry great risks for the patients involved. Mathematical models provide a...

Fall 2010

Cheng, Yin-Hei

Let $G$ be a locally compact group, $G^$ be the set of all extreme points of the set of normalized continuous positive definite functions of $G$ and $a(G)$ be the closed subalgebra generated by $G^$ in $B(G)$. When $G$ is abelian, $G^$ is the set of dirac measures of the dual group of $G$. The...

Fall 2021

Kosakian, Aslan

Hydrogen fuel cells convert the chemical energy of hydrogen directly into electricity, with the only byproducts being heat and water. The high cost of hydrogen fuel cells due to the expensive platinum catalyst is one of the limiting factors to their global commercialization. Improving fuel-cell...

Fall 2022

Liu, Shuo

This thesis concerns dynamical systems subject to small noise perturbations. Our purpose is to obtain a deep understanding of how small noise perturbations influence the original unperturbed dynamical system, especially over long but finite time intervals. We consider two special systems, the...

Fall 2013

Zeng, Linghang

This thesis focuses on characterizing an optimal trading strategy for a large trader, who has to buy (or sell) a fixed large volume over a given time period. We propose a model in discrete time, based on VWAP (Volume Weighted Average Price). The objective is to minimize expected deviations...

Fall 2020

Maher, Robert

The first part of this thesis presents an exposition of some of the links between integrability, matrix models and Airy structures. We first introduce the notion of an integrable hierarchy and a tau function. We then probe tau functions further by considering matrix integrals. These are...

Fall 2022

Weller, Quinten

The topological recursion is a construction in algebraic geometry that takes in the data of a so-called spectral curve, $\mathcal{S}=\left(\Sigma,x,y\right)$ where $\Sigma$ is a Riemann surface and $x,y:\Sigma\to\mathbb{C}_\infty$ are meromorphic, and recursively constructs correlators which, in...

Fall 2012

Kroll, Jeffrey P

This thesis is interested in the topological recursion first introduced in \cite{CEO} and generalized to algebraic curves in \cite{Eynard:2007,Eynard:2008}. A presentation of the Hermitian matrix model is given and includes a derivation of this topological recursion. The second part introduces a...