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Spring 2023

Xie, Zhangqian

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

Ge, Qi

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...

Fall 2023

Burak, Katherine

Many standard approaches for conducting statistical inference on regression parameters rely heavily on parametric assumptions and asymptotic results. The wild bootstrap (Mammen, 1993) was developed as a nonparametric means to estimate a sampling distribution and is particularly useful when...

Fall 2023

Stockall, Devon

The affine vertex superalgebra A=L^1(D(2,1;-v/w)) plays a key role as the geometric Langlands kernel VOA for SVOAs associated to so(3), osp(1|2) and other rank one Lie superalgbras. Since D(2,1;a) is an extension of the direct sum of 3 copies of sl(2), A can be naturally realized as an...

Fall 2023

Gervais, Alain D

A series of three studies investigates theoretically and numerically the evolution, stability, and pseudomomentum transport of fully localized three-dimensional internal gravity wave packets, as they self-interact nonlinearly with their induced mean flow. The first study considers a rotating,...

Fall 2023

Zhang, Junxi

Bayesian nonparametric models have gained increasing attention due to their flexibility in modelling natural and social phenomena and have been widely applied in machine learning, biology, social science and so on. Unlike traditional Bayesian parametric models, Bayesian nonparametric models place...

Fall 2023

Riesen, Andrew

$G$-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 Eilenberg-Maclane's notion of an Abelian $3$-cocycle to...

Fall 2023

Liu, Wenyue

As one type of principal-agent problem, the insurance contract models are closely related to the extent of information disclosure. We construct two new insurance contract models with full information and adverse selection respectively. The full information model is a continuous-time model in...

Fall 2023

Shyntar, Alexandra

In this thesis, we perform a systematic study of the Allee effect in cancer stem cell (CSC) models with an application to non-small cell lung cancer (NSCLC). Previously, it was shown that an Allee effect exists in mathematical tumor growth models incorporating cancer stem cell (CSC) dynamics....

Fall 2023

Liu, Yi

This thesis presents a comprehensive study of Gaussian Differential Privacy (GDP) and Local Differential Privacy (LDP), exploring their properties, relationships, and applications in developing novel algorithms and optimization methods for efficient and accurate privacy-preserving data analysis....