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Examining Whether Method Of Suicide Exposure And Closeness To Decedent Relate To Firearm Storage Practices, Evan A. Albury, Jessica L. Gerner, David A. Jobes, Raymond P. Tucker Apr 2025

Examining Whether Method Of Suicide Exposure And Closeness To Decedent Relate To Firearm Storage Practices, Evan A. Albury, Jessica L. Gerner, David A. Jobes, Raymond P. Tucker

Faculty Publications

Introduction: One factor that can influence whether someone will engage in secure firearm storage is having a suicide exposure (SE). Daruwala et al. (2018) examined this and found that individuals with an SE, without considering perceived closeness, did not significantly differ from those who did not have an SE in their firearm storage practices. Thus, the present study aimed to replicate and extend the research of Daruwala et al. (2018) by examining if the method of suicide (by firearm or other means) and closeness of suicide decedent relate to secure firearm storage practices. Methods: 308 male firearm owners completed self-report …


Exact Inference For Transformed Large-Scale Varying Coefficient Models With Applications, Tianyu Chen, Robert Habans, Thomas Douthat, Jenna Losh, Lida Chalangar Jalili Dehkharghani, Li Hsiang Lin Apr 2025

Exact Inference For Transformed Large-Scale Varying Coefficient Models With Applications, Tianyu Chen, Robert Habans, Thomas Douthat, Jenna Losh, Lida Chalangar Jalili Dehkharghani, Li Hsiang Lin

Faculty Publications

Studying migration patterns driven by extreme environmental events is crucial for building a sustainable society and stable economy. Motivated by a real dataset about human migrations, this paper develops a transformed varying coefficient model for origin and destination (OD) regression to elucidate the complex associations of migration patterns with spatio-temporal dependencies and socioeconomic factors. Existing studies often overlook the dynamic effects of these factors in OD regression. Furthermore, with the increasing ease of collecting OD data, the scale of current OD regression data is typically large, necessitating the development of methods for efficiently fitting large-scale migration data. We address the …


Polarization-Resolved Core Exciton Dynamics In Lif Using Attosecond Transient Absorption Spectroscopy, Kylie J. Gannan, Lauren B. Drescher, Rafael Quintero-Bermudez, Navdeep Rana, Chengye Huang, Kenneth Schafer, Mette B. Gaarde, Stephen R. Leone Apr 2025

Polarization-Resolved Core Exciton Dynamics In Lif Using Attosecond Transient Absorption Spectroscopy, Kylie J. Gannan, Lauren B. Drescher, Rafael Quintero-Bermudez, Navdeep Rana, Chengye Huang, Kenneth Schafer, Mette B. Gaarde, Stephen R. Leone

Faculty Publications

The ability to control absorption by modifying the polarization of light presents an exciting opportunity to experimentally determine the orbital alignment of absorption features. Here, attosecond extreme ultraviolet (XUV) transient absorption spectroscopy is used to investigate the polarization dependence of core exciton dynamics in LiF thin films at the Li+K edge. XUV pulses excite electrons from the Li 1s core level into the conduction band, allowing for the formation of a p-orbital-like core exciton, aligned along the XUV light polarization axis. A sub-5 fs near-infrared (NIR) probe pulse then arrives at variable time delays, perturbing the XUV-excited states and allowing …


Resonant Propagation Of Extreme-Ultraviolet Pulses Through Strongly Driven High-Density Media, Yu He, Shuyuan Hu, Gergana D. Borisova, Yizhu Zhang, Marc Rebholz, Zuoye Liu, Mette B. Gaarde, Christian Ott, Thomas Pfeifer Apr 2025

Resonant Propagation Of Extreme-Ultraviolet Pulses Through Strongly Driven High-Density Media, Yu He, Shuyuan Hu, Gergana D. Borisova, Yizhu Zhang, Marc Rebholz, Zuoye Liu, Mette B. Gaarde, Christian Ott, Thomas Pfeifer

Faculty Publications

We show that by combining strong-field dressing and resonant propagation of XUV pulses, the transition of absorption lines from their natural Lorentzian profiles through Fano and complex multipeak shapes all the way back to broadened near-Lorentzian profiles can be achieved, in the limit of optically thick samples. The final stage of this spectral modification can be understood in terms of a significant temporal stretching and delay of the resonant XUV pulse as it propagates through the dense gas, which alters the ultrafast absorption that is modified by the time-synchronized few-femtosecond laser pulse. We first demonstrate this concept in numerical calculations, …


Monitoring Molecular Interactions With Cell Membranes Using Time-Dependent Second Harmonic Generation Microscopy, Prakash Hamal, Sushant P. Sahu, Peter P. Piers, Huy Nguyen, Shashank S. Kamble, Robin L. Mccarley, Manas R. Gartia, Louis H. Haber Apr 2025

Monitoring Molecular Interactions With Cell Membranes Using Time-Dependent Second Harmonic Generation Microscopy, Prakash Hamal, Sushant P. Sahu, Peter P. Piers, Huy Nguyen, Shashank S. Kamble, Robin L. Mccarley, Manas R. Gartia, Louis H. Haber

Faculty Publications

Time-resolved second harmonic generation (SHG) microscopy is used to investigate the physicochemical interactions between positively charged, hydrophobic, drug-like molecules and the plasma membrane of human cells (nonsmall cell lung cancer, H596). In the present study, molecular adsorption and transport of the cationic molecules, malachite green (MG) and malachite green isothiocyanate (MGITC), are studied in real time in living H596 cells and in dead, fixed H596 cells. MGITC is shown to have stronger adsorption and more rapid transport kinetics as compared to MG due to increased dipole-dipole interactions. Additionally, MGITC is found to have faster adsorption and transport kinetics in living …


Introduction: The Future Of Global Journalism—Relationships, Tools, And Power, Ruth Moon, Lea Hellmueller, Herman Wasserman Apr 2025

Introduction: The Future Of Global Journalism—Relationships, Tools, And Power, Ruth Moon, Lea Hellmueller, Herman Wasserman

Faculty Publications

No abstract provided.


Unveiling The Nexus Between Digital Monitoring And Experiences Of Intimate Partner Violence In Romantic Relationships, Caley Hewitt, Fanny A. Ramirez, Anna Gjika Apr 2025

Unveiling The Nexus Between Digital Monitoring And Experiences Of Intimate Partner Violence In Romantic Relationships, Caley Hewitt, Fanny A. Ramirez, Anna Gjika

Faculty Publications

Using survey data from a sample of 378 women who live in the United States and self-identify as either Black or Latinx, this study explores predictors of women’s digital monitoring practices in intimate relationships in the context of intimate partner violence (IPV). We use literature about surveillance, monitoring, and IPV to frame our study. Our results show three significant instances that influence the odds of monitoring a romantic partner: (1) past experiences with digital abuse, (2) past experiences with offline psychological abuse, and (3) age, with younger women having increased odds of engaging in digital monitoring compared to older women. …


The Recusant's Dream, Isabella Temperville Apr 2025

The Recusant's Dream, Isabella Temperville

LSU Master's Theses

The Recusant’s Dream is a collection of works that portray the overarching lore of an original narrative by Isabella Temperville. Inspired by Biblical narratives, The Recusant’s Dream tells the story of Lucifer’s rebellion against an order of power-hungry archangels and the consequences that follow in the form of an all-consuming curse. The curse is both a marker and a death sentence, as those who bear it are called “demons” and are fated to eventually succumb to it. Lucifer was the first to fall victim to the consumption and his death sparked an infernal war amongst the cursed and the order …


Audience Participation Structures In The Concert Hall And D, Me, You, We, A Non-Opera For Actor, Chatbot, Musicians, And Audience, Treya Michelle Nash Apr 2025

Audience Participation Structures In The Concert Hall And D, Me, You, We, A Non-Opera For Actor, Chatbot, Musicians, And Audience, Treya Michelle Nash

LSU Doctoral Dissertations

Audience participation in the concert hall space has developed into a rich participatory practice with specific characteristics and challenges. Though composers—especially since the 1960s—have written many pieces involving audience participation, asking the concert hall audience to participate remains uncommon. Attempting to shift the role of the audience in such a traditionally spectator-oriented space can lead to tensions that undermine the efficacy of the experience. This research categorizes participatory pieces into the structural elements of performance and facilitation forces, audience groupings, audience roles, and communication types. These structures are used to discuss the complicated relationship between control and agency within participatory …


Approximations Of Koopman Operator Semigroups, Ibrahem Al Jabea Apr 2025

Approximations Of Koopman Operator Semigroups, Ibrahem Al Jabea

LSU Doctoral Dissertations

The main purpose of this dissertation is to study approximation methods for nonlinear systems using Bernhard Koopman's Global Linearization Method or Sophus Lie's method of continuous transformation groups. This approach enables the application of linear semigroup methods to a nonlinear system by focusing on the dynamics of the observables of the states, rather than directly studying the dynamics of the states. In this dissertation, we studied the pointwise semigroup and introduce the modified space $C_m(\Omega)$ and the modified Koopman-Lie semigroups. We use a splitting operator and outline a systematic approach for approximating the pointwise Koopman-Lie semigroup flows \begin{equation*} t\to T(t)g(x) …


19ne Excited States In Explosive Nucleosynthesis, Khang Pham Apr 2025

19ne Excited States In Explosive Nucleosynthesis, Khang Pham

LSU Doctoral Dissertations

Classical novae and Type I X-ray bursts are stellar explosions that occur in binary systems, where nuclear reactions involving 19Ne play a crucial role in nucleosynthesis. In novae, the destruction of 18F via the 18F(p,alpha)15O reaction significantly affects the amount of 18F remaining in the ejecta, directly influencing the detectability of predicted 511-keV gamma rays. However, discrepancies between observed and predicted 18F abundances highlight uncertainties in the reaction rates, primarily due to unknown properties of resonances in the compound nucleus 19Ne. In Type I X-ray bursts, the 15O(alpha,gamma)19Ne reaction …


The Passive-Active Interaction (Pai) Model: Redefining Audio Interactions In Video Game Music, Morgan A. Weeks Apr 2025

The Passive-Active Interaction (Pai) Model: Redefining Audio Interactions In Video Game Music, Morgan A. Weeks

LSU Doctoral Dissertations

Scholarship on music in video games has focused on the player in two main ways: the psychological effect music has on the player and the physical, kinesthetic relationship between the player’s inputs and the game’s music. This dissertation builds on this work by exploring gameplay moments in which the music informs the player’s inputs through rhythms, tempo, harmonic relationships, and changes in the musical texture. Using “analytical play” (Summers 2016), rhythmic analysis, looping analysis, and harmonic observations, alongside a variety of different video games, consoles and genres, I have developed an analytical Passive-Active Interaction (PAI) Model that is applicable to …


Unavoidable Immersions And Topological Minors Of K-Edge-Connected Graphs, Brittian Qualls Mar 2025

Unavoidable Immersions And Topological Minors Of K-Edge-Connected Graphs, Brittian Qualls

LSU Doctoral Dissertations

In this work, we present results concerning the unavoidable structures in large and infinite k-edge-connected graphs. These results are inspired by the classical result of Ramsey, who proved that for every positive integer r, every sufficiently large graph contains as an induced subgraph either Kr or $\overline{Kr}$. We consider different graph containment relations, focusing primarily on the immersion relation. In the case of finite graphs, we provide the unavoidable immersions of 4-edge-connected graphs and prove that linear edge-connectivity suffices to immerse the graph Ct,r.

This dissertation also considers infinite graphs. We present the …


The Influence Of Selected Demographic And Academic Factors On The Persistence To Degree Completion Of Military Veterans At A Research University In The South, Damon L. Ploger Mar 2025

The Influence Of Selected Demographic And Academic Factors On The Persistence To Degree Completion Of Military Veterans At A Research University In The South, Damon L. Ploger

LSU Doctoral Dissertations

A large number of veterans leave the military each year, hoping to reacclimate successfully to civilian society while utilizing the knowledge and skills they acquired in the military to assist in their pursuit of gainful employment. Many wish to enhance this process by earning a college degree. Unfortunately, various barriers and other random personal hurdles can impede the progress of the now-veteran student toward degree completion. The lack of knowledge about these barriers and the factors that support a veteran student’s persistence to complete a college degree has created the need for this investigation. The primary purpose of this study …


Optical Spring Tracking For Enhancing Quantum-Limited Interferometers, Scott M. Aronson Mar 2025

Optical Spring Tracking For Enhancing Quantum-Limited Interferometers, Scott M. Aronson

LSU Doctoral Dissertations

Gravitational waves were first predicted by Albert Einstein in 1916. Calculations in the 1970s by Rainer Weiss showed an interferometer of sufficient size could realistically detect gravitational waves, which led to a grant by the National Science Foundation (NSF). With steady progress and over decades of funding by the NSF, the construction of two full scale 4km interferometers was approved and began construction in 1994. This project, coined LIGO the Laser Interferometer Gravitational-wave Observatory, came to be a worldwide collaboration of scientists dedicated to the discovery and study of gravitational waves. In 2015, both LIGO detectors detected a coincident inspiral …


A Comprehensive Guide To A Trumpet Embouchure Change, Megan E. George Mar 2025

A Comprehensive Guide To A Trumpet Embouchure Change, Megan E. George

LSU Doctoral Dissertations

Abstract

The purpose of this project is to expand the literature related to the subject of trumpet embouchure change and provide a comprehensive resource that will assist both student and teacher in navigating a trumpet embouchure change. This resource will not only help them determine whether to go through with the process but will present them with multiple options regarding embouchure change starting methods. It can be used for a variety of ages but primarily intended for use with students high school age or older.

In current method books, one trumpet embouchure is usually presented and is often a “one-size-fits-all” …


Understanding The Experiences Of Biology Teachers During The Covid-19 Pandemic, Amber R. Collins Mar 2025

Understanding The Experiences Of Biology Teachers During The Covid-19 Pandemic, Amber R. Collins

LSU Doctoral Dissertations

ABSTRACT

The 2020 COVID-19 Pandemic has caused the world to focus on the transition of learning environments that are more digital and virtual than any other time in educational history. Schools all over the world were required to adjust not only the mode of instruction, such as in virtual, hybrid, or in-person, but also create guidelines and procedures that reduce the amount of interaction between the teacher and the student (Garbe, Ogurlu, Uzeyir, & Cook, 2020). The research questions that guided this study were: 1) What are the experiences of five Biology teachers during the COVID-19 pandemic in transitioning to …


The Role Of Mental Health Literacy And Social Media In Shaping University Students’ Intentions To Use Telehealth Services: A Theory Of Planned Behavior Approach In A Post-Pandemic Society, Jena R. Anderson Mar 2025

The Role Of Mental Health Literacy And Social Media In Shaping University Students’ Intentions To Use Telehealth Services: A Theory Of Planned Behavior Approach In A Post-Pandemic Society, Jena R. Anderson

LSU Master's Theses

This study examined the relationships between mental health literacy and social media use as an informational resource in college students and their intentions to use teletherapy. Using the theory of planned behavior as the framework, this research explores how attitudes towards teletherapy, subjective norms, and perceived behavioral control influence students' willingness to seek out mental health services such as teletherapy. Findings revealed that mental health literacy is a strong predictor of students' attitudes and perceived behavioral control, reinforcing prior research that links literacy to better health management among patients. Social media was also a strong predictor of subjective norms, highlighting …


Quantitative Risk Analysis For Elections, George A. Buras Mar 2025

Quantitative Risk Analysis For Elections, George A. Buras

LSU Master's Theses

This paper examines risk analysis and risk management in the field of election security. The purpose of this paper is not to enumerate risks to election security or explain how they might be mitigated, but rather to understand and improve how we measure and communicate those risks.

First, I contextualize election security risks by establishing what it means for an election to be secure and I give an overview of the types of events that might threaten election security. Then, I explore different methods that we can use to model electoral risks. Existing resources for managing electoral risks use qualitative …


Assessing Groundwater Availability And Land Subsidence Risk Associated With Anthropogenic Activities In A Complex Aquifer System, Aya Bakr Attya Mohamed Mar 2025

Assessing Groundwater Availability And Land Subsidence Risk Associated With Anthropogenic Activities In A Complex Aquifer System, Aya Bakr Attya Mohamed

LSU Doctoral Dissertations

The Southern Hills aquifer system (SHAS) is the primary source of water in the Capital area of Louisiana. However, the overexploitation of freshwater-bearing aquifers and the presence of two active faults, the BR fault and the DSS fault, have resulted in groundwater depletion, saltwater intrusion, and increased the risk of land surface subsidence. Such critical issues pose substantial threats to groundwater availability and exert detrimental effects on the environment and urban infrastructures. This dissertation presents a comprehensive investigation of the SHAS for recognizing the consequences of groundwater depletion and its potential long-term impacts on groundwater availability and land stability. A …


Adverse Childhood Experiences And High School Dropout: The Roles Of Student Disengagement And Social Support, Rachel D. Pounders Mar 2025

Adverse Childhood Experiences And High School Dropout: The Roles Of Student Disengagement And Social Support, Rachel D. Pounders

LSU Doctoral Dissertations

More than two million students a year leave high school without a completion credential (NCES, 2024). Students who drop out are at-risk for detrimental long-term outcomes physically, mentally and economically (Rumberger, 2020). Students with adverse childhood experiences (ACEs) are significantly more likely to have poor educational outcomes, including school dropout (Metzler et al., 2017; Pan et al., 2019). However, there is limited insight into what affects the pathway between ACEs and poor educational outcomes for students (Dupéré et al., 2019; Morrow & Villodas, 2018). Informed by prominent dropout theories with ecological foundations and the theory of stress and coping, this …


Studies On Cell Cycle Regulation And Ecm Modification During Tubular Organ Formation In Drosophila Embryos, Jeffrey Matthew Mar 2025

Studies On Cell Cycle Regulation And Ecm Modification During Tubular Organ Formation In Drosophila Embryos, Jeffrey Matthew

LSU Doctoral Dissertations

The formation of tubular organs—such as the heart and kidneys—is a complex developmental process that requires the precise coordination of tissue remodeling with dynamic changes in cellular behavior. Key processes including cell proliferation, apoptosis, and extracellular matrix (ECM) formation must be tightly synchronized with mechanisms that generate and transmit physical forces, transforming a flat epithelial sheet into a three-dimensional organ. Disruptions in the homeostasis of these processes during organogenesis can lead to congenital defects, such as pulmonary atresia and renal hypoplasia.

To investigate the mechanisms underlying epithelial morphogenesis, the Chung laboratory employs the Drosophila embryonic salivary gland (SG) as a …


Voices Of Heritage And Resilience: A Performance Guide To Soprano Arias Celebrating The Black Experience In Opera, Imani S. Francis Mar 2025

Voices Of Heritage And Resilience: A Performance Guide To Soprano Arias Celebrating The Black Experience In Opera, Imani S. Francis

LSU Doctoral Dissertations

Voices of Heritage and Resilience: A Performance Guide for Soprano Arias Celebrating the Black Experience explores a selection of soprano arias that illuminate the depth, complexity, and resilience of Black identity through opera. This study provides historical context, musical style, and vocal performance strategies for works that center around the African American experience, spanning both traditional and contemporary repertoire.

By examining the relations between text, music, and historical significance, this dissertation highlights how these arias convey themes of struggle, conflict, oppression, love, and perseverance. It also supplies guidance to the singer through the use of vocal methods, interpretation, and stylistic …


Quaternary Subsurface Characterization Of The Mississippi River Valley Alluvial Aquifer: Insights From Interval Kriging And Airborne Em-Borehole Data Integration, Yuqi Song Mar 2025

Quaternary Subsurface Characterization Of The Mississippi River Valley Alluvial Aquifer: Insights From Interval Kriging And Airborne Em-Borehole Data Integration, Yuqi Song

LSU Doctoral Dissertations

The Pleistocene period significantly contributed to the formation of alluvial aquifer worldwide. These productive aquifers are crucial for domestic, industrial, and agricultural water supplies. The Mississippi River Valley alluvial aquifer (MRVA), a principal aquifer in the U.S., is crucial for national food security and global agricultural supply. This study aims to characterize the subsurface architecture of the MRVA, thereby enhancing fundamental understanding of sedimentological processes involved in the genesis of glacio-fluvial aquifers worldwide. The research objectives are threefold: (1) to provide a detailed characterization of the MRVA; (2) to develop 3D geostatistical methods for geological modeling; and (3) to develop …


On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis Mar 2025

On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis

LSU Doctoral Dissertations

The Boltzmann equation describes the time evolution of the density function in position-velocity space for a classical particle subjected to possible collisions by other particles in a diluted gas that expands in vacuum for a given initial distribution. While many authors have studied the probabilistic interpretation of the spatially homogeneous Boltzmann equation, there is a dearth of articles on the stochastic framework of the full (that is, spatially inhomogeneous) Boltzmann equation. In this thesis, we examine a stochastic process, developed by S. Albevario, B. Ruediger, and P. Sundar, whose law is a weak solution to a mollified Boltzmann equation. This …


On Unavoidable Infinite Hypergraphs, Samuel Weiner Mar 2025

On Unavoidable Infinite Hypergraphs, Samuel Weiner

LSU Doctoral Dissertations

Ramsey's Theorem states that every infinite graph contains either K∞ or $\overline{K∞}$ as an induced subgraph. For this reason, K∞ and $\overline{K∞}$ are often referred to as the unavoidable infinite graphs. Many similar results have characterized the unavoidable members for various classes of infinite graphs; perhaps the most notable of these is König's Infinity Lemma, which states that every infinite, connected, locally finite graph contains a ray as an induced subgraph. From these findings, one can easily deduce that every infinite, connected graph contains an infinite clique, star, or ray as an induced subgraph; …


Exploring Pedagogical Approaches And Discussion For Young Beginner Double Bass Players, Jiaying Zhang Mar 2025

Exploring Pedagogical Approaches And Discussion For Young Beginner Double Bass Players, Jiaying Zhang

LSU Doctoral Dissertations

In recent years, early childhood education for the double bass has gained increasing attention and plays a crucial role in shaping the future development of the instrument. However, compared to other instruments, research on early childhood education for the double bass remains relatively underdeveloped, with a lack of written materials on the subject. This thesis introduces the formation of early childhood teaching concepts and explains why parents play an irreplaceable role in a child’s initial exposure to music learning. By collecting and analyzing traditional double bass teaching methods and integrating common principles from other string instrument teaching approaches, this study …


Rheological, Interfacial, And Filtration Behavior Of Lignocellulosic Nanomaterials In Suspension And Emulsion Drilling Fluids, Meen Sung Koo Mar 2025

Rheological, Interfacial, And Filtration Behavior Of Lignocellulosic Nanomaterials In Suspension And Emulsion Drilling Fluids, Meen Sung Koo

LSU Doctoral Dissertations

In recent years, the rheological aspects of suspensions/emulsions applied by cellulose nanomaterials (CNMs) have been gained considerable interests due to high gel-forming properties ascribed by hydrophilicity, crystallinity, ease functionalization, and high aspect ratio. Introducing residual lignin in CNMs (LCNMs) seemed to be capable of achieving various advantages in the application of CNMs ascribed by hydrophobicity, binding effects, and abundant aromatic groups derived from complexity of lignin. This dissertation dedicates to the characterizations of (L)CNMs, and rheological properties of (L)CNMs applied fluids (i.e., suspension and emulsion). In the suspension system, the presence of lignin in LCNMs decreased gel strength, viscosity, and …


Evaluating Biotic Effecrs Associated With The Paleocene-Eocene Thermal Maximum In Mississippi And Alabama: A Palynological And Biostratigraphic Study Of Amoco's Legacy Samples, Sarah Fortin Bancroft Mar 2025

Evaluating Biotic Effecrs Associated With The Paleocene-Eocene Thermal Maximum In Mississippi And Alabama: A Palynological And Biostratigraphic Study Of Amoco's Legacy Samples, Sarah Fortin Bancroft

LSU Master's Theses

The Paleocene-Eocene Thermal Maximum (PETM) was a ~200 ka period of rapid global warming in the earliest Eocene (~56 Ma) involving a roughly 7 °C rise in atmospheric and sea-surface temperatures. The Gulf of Mexico Wilcox Group contains very well-preserved terrestrial and deltaic sediments that contain exploitable hydrocarbons . The Wilcox Group’s Paleocene Tuscahoma and Eocene Hatchetigbee Formations have been roughly dated with calcareous and planktonic foraminiferal assemblages by AMOCO; however, the precise ages of these formations, their palynological assemblages, and their paleo-depositional geosystems are an area of active research.

Through a high-resolution palynological analysis, this study assesses the depositional …


Explicit Modularity And Moments For Certain Hypergeometric Character Sums, Brian Grove Mar 2025

Explicit Modularity And Moments For Certain Hypergeometric Character Sums, Brian Grove

LSU Doctoral Dissertations

A great deal of progress in number theory throughout history has been motivated by trying to solve equations. One of the most famous challenges is to show there are no positive integer solutions to $x^{n}+y^{n} = z^{n}$ for $n > 2$, posed by Fermat around 1637. Special cases, such as the $n = 3$ and $n = 4$ cases, can be established using various algebraic manipulations. However, a general solution was elusive until the late 1990s when the combined work of Wiles \cite{Wiles} and Taylor--Wiles \cite{TaylorWiles} give a full proof.

One of the key insights used in proving Fermat's conjecture involves …