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 2Department of Biological Sciences
 2Department of Mechanical Engineering
 1Department of Civil and Environmental Engineering
 1Department of Computing Science
 1Department of Public Health Sciences
 7Frei, Christoph (Mathematical and Statistical Sciences)
 7Hillen, Thomas (Mathematical and Statistical Sciences)
 7Kong, Linglong (Mathematical and Statistical Sciences)
 7Lewis, Mark (Mathematical and Statistical Sciences)
 6Han, Bin (Mathematical and Statistical Sciences)
 6Kashlak, Adam (Mathematical and Statistical Sciences)

Fall 2022
The Helmholtz equation is a fundamental wave propagation model in the timeharmonic setting, which appears in many applications such as electromagnetics, geophysics, and ocean acoustics. It is challenging and computationally expensive to solve due to (1) its highly oscillating solution and (2)...

Fall 2022
In this dissertation, various problems related to stochastic (partial) differential equations are investigated. These problems include wellposedness, H\"older continuity of the solution, moments of the solution and their asymptotics. This thesis is divided into three parts. The first part...

A Universal Approximation Theorem for Tychonoff Spaces with Application to Spaces of Probability and Finite Measures
DownloadFall 2022
Universal approximation refers to the property of a collection of functions to approximate continuous functions. Past literature has demonstrated that neural networks are dense in continuous functions on compact subsets of finitedimensional spaces, and this document extends those findings to...

Fall 2022
Interface problems arise in many applications such as modeling of underground waste disposal, oil reservoirs, composite materials, and many others. The coefficient $a$, the source term $f$, the solution $u$ and the flux $a\nabla u\cdot \vec{n}$ are possibly discontinuous across the interface...

Fall 2022
The topological recursion is a construction in algebraic geometry that takes in the data of a socalled 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...

Spring 2022
This work develops numerical methods (finite difference methods) for equations of fluid dynamics and equations of elasticity reformulated in the stress variables (as opposed to natural variables) and applies them to the FluidStructure Interac tion (FSI) problem using a new model based on the...

Spring 2023
In present thesis I focus on development of method of market completions and its applications to various problems in pricing and hedging of contingent claims. Since theory of mathematical finance is well developed on complete markets, and corresponding solutions are well understood, method of...

Spring 2023
Credit risk management, which deals with mitigating losses from lending activities, is crucial for financial institutions. Hence, credit risk modelling can be employed to reduce potential losses and avoid financial crises. There are sometimes monotonic relationships in credit risk models, which...

Fall 2023
This dissertation establishes various structural and representation theoretic results in super Yangian theory. In its first part, this dissertation details the algebraic structure and representation theory for the Yangians of orthosymplectic Lie superalgebras. Addressing these Yangians via the...

Fall 2023
$G$structures on fusion categories have been shown to be an important tool to understand orbifolds of vertex operator algebras \cite{Kirillov}\cite{Gcrossedmuger}\cite{Orbifold_Paper}. We continue to develop this idea by generalizing EilenbergMaclane's notion of an Abelian $3$cocycle to...