Research

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Ph.D. Dissertations

Continuous dependence on modeling for ill-posed evolution problem, Matthew Fury, 2010. Advisor: Rhonda Hughes.
Relative Knovanov-Jacobsson classes for spanning surfaces, Jonah Swann, 2010. Advisor: Paul Melvin.
Bounding the number of solutions to tetranomial Thue equations, Daniel Wisniewski, 2010. Advisor: Helen Grundman.
Lp Estimates for Oscillatory Singular Integral Operators and Marcinkiewicz Integral Operators, Ayako Fukui, 2009. Advisor: Leslie Cheng.
Determining Lower Bounds for Packing Densitites of Non-Layered Patterns Using Weighted Templates, Cahtleen Battiste-Presuitti, 2008 Advisor: Walter Stromquist.
Legendrian Torus Links, Jennifer Dalton, 2008. Advisor: Lisa Traynor.
The Existence of Elliptic periodic Orbits in the Smoothed Bunimovich Stadium, Sherry Teti, 2008. Advisor: Victor Donnay.
Continuous Dependence Results for Inhomogeneous Ill-Posed Problems, Beth Campbell-Hetrick, 2006. Advisor: Rhonda Hughes.
Generating Family Invariants for Legendrian Links, Jill Jordan, 2005. Advisor: Lisa Traynor.
Smooth Approximation of Singular Perturbations of the Laplacian, Walter Huddell, 2002. Advisor: Rhonda Hughes.
The Arithmetic Genus of Threefolds Defined by Extended Hilbert Modular Groups, Amber Salzman, 2002. Advisor: Helen Grundman.
Symplectic Packings of Cotangent Bundles of Tori, Jean Mastrangeli, 1997. Advisor: Lisa Traynor.
Sewn up and Surgered Swen up Link Exteriors: Surgery Presentations & Formulas for Lescop’s Invariant, Gowri Meda, 1997. Advisor: Paul Melvin.

M.A. Theses

Expansion of Boundedness Results for Certain Oscillatory Integral Operators, Lise Chlebak, 2011. Advisor: Leslie Cheng.
Galois Groups of Certain Polynomials of Prime Degree, Rebecca Rebhuhn-Glanz, 2011. Advisor: Helen Grundman.
Mathematical Modeling of Malaria, Amy Veprauskas, 2010. Advisor: Victor Donnay.
On the Boundedness of Certain Oscillatory Integral Operators, Manal Zaher, 2010. Advisor: Leslie Cheng.
Properties of Class Groups of a Family of Cyclic Cubic Fields, Jaclyn Lang, 2009. Advisor: Helen Grundman.
On the Boundedness of Oscillatory Integral Operators in Harmonic Analysis, Sarah Khasawinah, 2009. Advisor: Leslie Cheng.
Solutions to a Parametrized Family of Relative Thue Equations, Amanda Hittson, 2009. Advisor: Helen Grundman.
Aditi Vashist, 2008
A New Proof of the Spectral Theorem, Milena Redzic, 2008. Advisor: Rhonda Hughes.
Thomas's Work on Split Families of Cubic Thue Equations, Wen Gao, 2007. Advisor: Helen Grundman.
Lp Boundedness of Oscillatory Integral Operators, Anna Gordon, 2007. Advisor: Leslie Cheng.
Applications of Heatlets to Ill-Posed Problems, Emily McNabb, 2007. Advisor: Rhonda Hughes.
Kirsten Kemp, 2006.
Class Numbers and Other Numerical Invariants of Imaginary Quadratic Fields, Laura Hall, 2004. Advisor: Helen Grundman.
Morse Theory, Kim Urso, 2004. Advisor: Lisa Traynor.
Producing Positive Lyapunov Exponents on the Sphere, Gina Calderaio, 2003. Advisor: Victor Donnay.
Constructing Brownian Motion with Wavelets, Beth Campbell, 2002. Advisor: Rhonda Hughes.
Chekanov’s Decomposition Invariant for Legendrian Knots, Jane Holsapple, 2002. Advisor: Lisa Traynor.
Power Basis Generators in Cyclotomic Fields, Jill Jordan, 2002. Advisor: Helen Grundman.
Weight Systems, Rachael Thomas, 2001. Advisor: Paul Melvin.
On Galois Realizability of Groups of Order 32, Grisha Stewart, 2001. Advisor: Helen Grundman.
Weighted Lp -Lq Inequalities for Oscillatory Integral Operators, Lisa Marchisio, 2004. Advisor: Leslie Cheng
Valuation of Asian Options: Monte Carlo Simulation, Ayako Fukui, 2003. Advisor: Leslie Cheng
On a Study of Oscillatory Integral Operators, Shrooti Singh, 2003. Advisor: Leslie Cheng.

A.B./M.A. Theses

On Slice Obstructions for Unknotting Number One Knots, Avalon Vanis, 2023. Advisor: Melvin
Origami with Infinite Folds, Elizabeth Hankins, 2022. Advisor: Donnay
Sums of Products of Kloosterman Sums, Ada Marcovitz, 2022. Advisor: Milićević.
Modeling the Effects of Incretins and Circadian Misalignment on Glucose-Insulin Dynamics, Ryann McManus, 2022. Advisor: Graham
Numerical Methods in Issues of Sustainability, Shefali Ramakrishna, 2022. Advisor: Donnay.
Hecke Operators on Linear Representations Over Finite Fields, Sophia Schein, 2020. Advisor: Bergdall.
p-adic Analysis and Supercongruences to Higher Prime Power Moduli, Aisha Mechery, 2019. Advisor: Milićević.
Distribution of Kloosterman Paths to High Prime Power Moduli, Cheyenne (Sichen) Zhang, 2019. Advisor: Milićević.
Exploring Oscillatory Integral Operators for Functions in Higher Dimensions, Sarah Gift 2018. Advisor: Cheng.
Statistics of Perturbed Laplacian Eigenfunctions, Boyang Su, 2018. Advisor: Milićević.
Cases of Effective Nonvanishing of Dirichlet L-Functions Over Primitive Galois Orbits, Ruoyun Lei 2017. Advisor: Milićević.
Normal Rulings of Legendrian Satellite Knots, Madeleine Hanson-Colvin, 2016. Advisor: Traynor.
Valuation of Lookback Options, Emily Schroeter, 2015. Advisor: Cheng.
Stochastic Processes and Valuation of Options, Freda Li, 2014. Advisor: Cheng.
New Results in Inverse Galois Theory, Katherine Engelman, 2014. Advisor: Grundman.
Stochastic Processes and Pricing Derivatives in Continuous Time, Yolanda Shao 2013. Advisor: Cheng.
Galois Groups of Certain Polynomials of Prime Degree, Rebecca Rebhuhn-Glanz, 2011. Advisor: Grundman.
Expansion of Boundedness Results for Certain Oscillatory Integral Operators, Lise Chlebak, 2011. Advisor: Cheng.
On the Boundedness of Certain Oscillatory Integral Operators, Manal Zaher, 2010. Advisor: Cheng.
Mathematical Modeling of Malaria, Amy Veprauskas 2010. Advisor: Donnay.
Properties of Class Groups of a Family of Cyclic Cubic Fields, Jaclyn Lang, 2009. Advisor: Grundman.
Lp Boundedness of Oscillatory Integral Operators, Sarah Khasawinah, 2009. Advisor: Cheng.
Solutions to a Parameterized Family of Relative Thue Equations, Amanda Hittson, 2009. Advisor: Grundman.
Torsion in Khovanov Homology, Aditi Vashist, 2008. Advisor: Melvin.
Applications to Heatlets to Ill-Posed Problems, McNabb, Emily 2007. Advisor: Hughes.
Lp Boundedness of Oscillatory Integral Operators, Anna Gordon, 2007. Advisor: Cheng.
Thomas's Work on Split Families of Cubic Thue Equations, Wen Gao, 2007. Advisor: Grundman.
Lp Estimates for Oscillatory Integral Operators, Kirsten Kemp, 2006. Advisor: Cheng.
Arnold's 4-Cusp Conjecture, Devasish Majumdar, 2005. Advisor: Lisa Traynor.
Tangling Legendrian Knots, Cristina Nistor, 2005. Advisor: Paul Melvin.
The Arnold Invariants of Plane Curves, Emi Arima, 2005. Advisor: Lisa Traynor
A Simple-Homotopy Classification of Certain CW-Complexes by Reidemeister Torsion, Ben Allen, 2002. Advisor: Paul Melvin.

Honors Theses

Cost-Benefit Analysis of LED Conversion, Lisa Adanye. Advisor: Donnay.
Exploring Applications of Arbitrage: Finding Arbitrage Opportunities in a Financial Context and Exploiting Market Inefficiencies in Parimutuel Horse Races, Li Gordon-Washington. Advisor: Cheng.
Mathematics of Photoelasticimetry and Numerical Operation of the Photoelastic Grain Solver, Augustus Helson. Advisor: Cheng/Brzinski (HC).
Improved Computational Approach to Measuring the Tightness of Molecular Knots, Yesenia Hernandez. Advisor: Francl/Myer.
Chaotic Dynamical Systems: Theory and Visualization, Jasmine Lei. Advisor: Cheng/Normoyle.
The Prisoners' Dilemma, Alishia Nation. Advisor: Cheng.
Partial Differential Equation: Solution and Applications, Minh Anh Nguyen. Advisor: Cheng.
The Sum of the Products of Four Kloosterman Sums, Catherine Robinson. Advisor: Milićević.
Combinatorial Games: Nim, Wythoff's Game, Tape Dominoes, Simple Blokus, Lola Rodrigues. Advisor: Cheng.
Valuation of Options, Hayat Shibeshi. Advisor: Cheng.
Modeling Diabetes Using Symbolic Regression Techniques, Rosalie Tarsala. Advisor: Graham.
Mathematics of Hedging, Veronica Wang. Advisor: Cheng.

2022

Pricing Perpetual Barrier Options on Moderna, Pfizer, and Johnson & Johnson Stocks Using Microsoft Excel, Laila Ali. Advisor: Cheng.
Discrete Fourier Analysis, Sidney Bachrach. Advisor: Cheng.
An Application of Survival Model in Insurance, Marya Cruz. Advisor: Cheng.
Numerical Modeling with Iterative Methods for Ground Water Flow Equation, Trang Duong. Advisor: Donnay.
Trace Obstructions of Equidistributed Holonomy, Allison Eckert. Advisor: Milićević.
Lp Estimates for Oscillatory Integral Operators and Hörmander's Theorem, Zaynab Ghazi. Advisor: Cheng.
GBM Modeling of Renewable and Non-Renewable Energy Stocks, Amirah Hewitt. Advisor: Cheng.
The Mathematical Approach to Medical ImagingCheng.
The Mathematics of Financial Derivatives, Jocelyn Luo. Advisor: Cheng.
Valuation of Options, América Najera. Advisor: Cheng.
Portfolio Optimization, Tina Nguruve. Advisor: Cheng.
Application of Dual Quaternions to Skinning of Characters, Olga Shevchuk. Advisor: Traynor/Normoyle.

2021

The Distribution of Greatest Common Divisor of Elements in Z[√2], Sandy Chen. Advisor: Bergdall.
Mathematical Modeling of Pulmonary Thrombosis in COVID-19, Katie Coe. Advisor: Graham.
Bond Pricing Models, Aakriti Dhital. Advisor: Cheng.
Computationally Modeling the Human Complement System to Predict SARS-CoV-2 Immune Response, Samantha Hall. Advisors: Cheng/Radhakrishnan (UPenn).
Energy Investing: Comparing Renewable and Fossil Energy Company Stock Prices Using the Binomial Tree Model, Grayson Hamrick. Advisor: Cheng.
Valuation of Asian Options, Zhuoran Hu. Advisor: Cheng.
Valuation of Barrier Options, Edith Jepkirui. Advisor: Cheng.
Comparison of Hull-White Algorithm and Geometric Brownian Motion Using Six Chinese Stocks, Ziyi Li. Advisor: Cheng.
Arbitrage Theorems and Their Applications, Jiayang Lu. Advisor: Cheng.
American versus European Options, Joan Ndichu. Advisor: Cheng.
The Mathematics of Medical ImagingCheng.
Optimal Control Problems, Peiran Xu. Advisor: Traynor.
Modeling Cause of beta-amyloid Induced Alzheimer's Disease and Its Potential Treatment, Liwei Yang. Advisor: Graham.

2020

Modeling Air Pollution in Philadelphia Using Gaussian Plume Model and Diffusion Equations, Shannon Fisher. Advisor: Donnay.
Transverse Unknotting Number and Family Trees, Blossom Jeong. Advisor: Traynor.
Modeling Anchovy Interactions in the Puget Sound, Ellie Lee. Advisor: Graham.
Effectiveness of Isolation and Quarantine for COVID-19 in Wuhan from November 17, 2019 to March 31, 2020, Irene Lin. Advisor: Graham.
Mortality Modeling of NBA Players, Meagan Murray-Bruce. Advisor: Cheng.
Modeling Ebola Virus in West Africa using Differential Equations, Ody Oranekwu. Advisor: Donnay.
Portfolio Management, Shuning Wang. Advisor: Cheng.
Predicting Stock Prices Using Mathematical Models, Xiya Wei. Advisor: Cheng.
Stock Price Prediction for FAANG Stocks, Zhi Zheng. Advisor: Cheng.
Option Pricing and Hedging Strategies, Maggie Zhong. Advisor: Cheng.

2019

Predicting Stock Prices of Indian Pharmaceutical Companies, Namrata Basu. Advisor: Cheng.
An Analysis of the Relationship between Stock Market Development and Economic Growth in Nepal, Romy Dangol. Advisor: Cheng.
Modeling the Development and Transmission of HIV, Junyan Duan. Advisor: Donnay.
Fitzhugh-Nagumo Analysis, Hodgkin-Huxley Models, and Applications in GnRH Secretion, Natalie Meacham. Advisor: Donnay.
A Broad Overview of the Discrete Wavelet Transform in NMR Signal Processing, Leslie Reiffen. Advisor: Cheng.
Arbitrage in Financial Markets, Siraj Mehendi. Advisor: Cheng.
An Introduction to Khovanov Homology and Related Knot Invariants, Xingya Wang. Advisor: Melvin.

2018

Optimal Control Theory: Finding the Optimal Cancer Treatment Protocol for Various Anti-Cancer Approaches, Dina Benedetto. Advisor: Graham.
Portfolio Selection Problem: Optimal Portfolio and Minimum Analysis Approach, Linh Nguyen. Advisor: Cheng.
An Application of Queueing Theory: Optimizing Queues at JFK Airport, Phuong Nguyen. Advisor: Graham.
Valuation and Hedging of Barrier Options, Thu Nguyen. Advisor: Cheng.
Mathematical Methods of Studying Disease: Formal and Statistical Approaches, Hunter Rendelman. Advisor: Cheng.
On Some Supercongruence Conjectures for Hypergeometric Series, Yu Sheng. Advisor: Milićević.
Valuation of Lookback Options on LVMH Stock, Rachel Terry. Advisor: Cheng.
Persistent Homology: From Data to Barcodes, Wenqi Wang. Advisor: Melvin.

2017

Pricing Up-And-Out Call Options, Yiling Bai. Advisor: Cheng.
An Analysis of the Viability of Wind TurbinesDonnay.
Valuation of Lookback Options, Prianka Ball. Advisor: Cheng.
Multi-crossing Projections of Legendrian Knots, Tianyi He. Advisor: Traynor.
Well-Quasi Ordering and its Relation to Terminating Rewrite System, Jingling Li. Advisor: Cheng.
Chaotic Systems of Geodesics on Surfaces of Revolution, Westley Mildenhall. Advisor: Donnay.
Well-Quasi Ordering and Confluence, Kewei Qu. Advisor: Cheng.
Generalized Two-parameter Exponential Distribution and its Parameter Estimation, Yichen Wang. Advisor: Cheng.

2016

Estimation Maximization Algorithm: Its Application and Implementation in R, Xiaoqi Geng. Advisor: Nancy Zhang at UPenn.
Harshad Numbers and Shantid NumbersGrundman.
Persistent Homology and Its Application to Data Analysis, Melina Koukoutchos, Advisor: Melvin.
Financial Models: Theory with Examples using Real Data, Bingxi Lin. Advisor: Cheng.
Applications of the Hull-White One-Factor Model, Yamina Mohattane. Advisor: Cheng.
An Introduction to Computational Persistent Homology, Shuhong (Paula) Sun. Advisor: Melvin.
Portfolio Management with a Focus on Monte Carlo Simulation, Siran Tang. Advisor: Cheng.
Generalizations of Happy Numbers, Simon Williams. Advisor: Grundman.
Immunological HIV/AIDS Modeling and Tumor Modeling, Wanqing Wu. Advisor: Donnay.
Geometric Brownian Motion in Financial Mathematics, Ziyi Yan. Advisor: Cheng.
A Development of Basic Stochastic Calculus and its Applications, Yuping Zhai. Advisor. Cheng.

2015

Surgery Strings of Legendrian Knots, Orsola Capovilla-Searle. Advisor: Traynor.
Stock Price Movement: Simulations and Theories, Xinyuan Dong. Advisor: Cheng.
Geodesic Path of a Surface of RevolutionDonnay.
New p-adic Sextic Supercongruences of Ramanujan Type, Madeleine Johnson. Advisor: Milićević.
Valuation of American Options, Yifan Liu. Advisor: Cheng.
Option Valuation Under Risk Neutral Measures, Danqi Luo. Advisor: Cheng.
Analyzing Music Through Geometry, Swetha Narasimhan. Advisor: Traynor.
Powering Our Future with Sun and Wind: A Renewable Energy Model for Delaware, New Jersey, and Pennsylvania, Danielle Preziuso. Advisor: Donnay.
Fixed Point Theorems and Applications to Economics, Lipika Ramaswamy. Advisor: Traynor.
Mathematical Modeling of Ebola, Jessie Tang. Advisor: Donnay.

2014

A Development of Basic Stochastic Calculus and Its Applications, Taha Ahsin. Advisor: Cheng.
The Omega Primality Function in Consecutively Generated Embedding Dimension Three Monoids, or How Studying Chicken McNuggets Helped Me Explain Complex Algebraic Structure, Emelie Curl. Advisor: Cheng.
The Mathematics of Medical Imaging, Jeanne Mirbey. Advisor: Cheng.
Brownian Motion, Sookyung Oh. Advisor: Cheng.
Incomplete Character Sums, Kriti Shrestha. Advisor: Milićević.
City Network: The Dynamics of Location, Education, and Production, Sophie Zhao. Advisor: Traynor.

2013

Harmonic Analysis: the bounded Oscillatory Integrals, Lynne Ammar. Advisor: Cheng.
Games, Games, Games: Multistage Stochastic Games, Bianca Boranda. Advisor: Traynor.
Gonorrhea Transmission Dynamic and Netlogo Simulation, Hoang Ha. Advisor: Donnay.
Introduction of Valuation of Financial Derivatives, Hao Jiang. Advisor: Cheng.
Lp Estimates for a Certain Class of Oscillatory Integral Operators, Sunny Kang. Advisor: Cheng
Netlogo Simulations of HPV, Brenda Martinez. Advisor: Donnay.
Reproducing Kernal Hilbert Spaces in Multi-Task Machine Learning, Meagan Neal. Advisor: Cheng (jointly with Visiting Assistant Professor of Computer Science Eric Eaton).
Symmetry in Dance and Art: Group Theory and its Applications, Meghan Pandya. Advisor: Cheng.
Hedging using Options and Futures, Alisha Pradhan. Advisor: Cheng.
Mathematical Modeling of West Nile Virus and Climate Change, Hannah Weinstein. Advisor: Donnay.
Cooperative Games and the Nash Bargaining Model, Qian Wu. Advisor: Traynor.
Stochastic Process and Option Pricing Models, Pan Xie. Advisor: Cheng.
The Set of Signed Unknotting Numbers, Traynor. Advisor: Traynor.

2012

An Analysis of Energy Use in �鶹AV Buildings, Kaushiki Dunusinghe. Advisor: Donnay.
Vanilla and Exotic Options: Valuation and Hedging, Winniw Hien. Advisor: Cheng.
Guinea Worm Disease: Opening a mathematical can of worms, Katie Link. Advisor: Donnay.
An Inverse Zero-Sum Conjecture, Aidan Murphy. Advisor: Grundman.
Valuation of Options, Jennifer Savage. Advisor: Cheng.
A Theorem on the Weighted Davenport constant, Catherine Owens. Advisor: Grundman.
Oscillatory intergral Operators and Improved Hormander's Theorem, Jennifer Savage. Advisor: Cheng.
Options, Hedging and Portfolio Management, Tong Wu. Advisor: Cheng.

2011

Construction of Smooth Curves and Surfaces, Bethany Azuma. Advisor: Melvin.
Valuation of Barrier Options, Sasha Bereznak. Advisor: Cheng.
Modeling the Joint Epidemics of HIV and TB, Ellie Caniglia. Advisor: Donnay.
Mathematics in Medical Imaging, Sara Davidson. Advisor: Cheng.
Valuation of Options and Hedging, Romy Delwar. Advisor: Cheng.
Valuation of European and American Call Options, Anagha Kumar. Advisor: Cheng.
Configuration Spaces of Graphs, Alex Lee. Advisor: Traynor.
Mathematics in Crystallography, Adele Mirbey. Advisor: Cheng.
Using Phylogenetic Trees to Understand the Evolution of Genes, Alison Panosia. Advisor: Traynor.

2010

HIV - A Controllable Disease, Caitlin Iles. Advisor: Donnay.
Mathematical Modeling of Climate Change: Examining the Diurnal Temperature Range, Naomi Hamermesh. Advisor: Donnay.
The Mathematics of Catastrophe Risk, Alyssa Martin. Advisor: Cheng.
Why ESPN Needs More Mathematicians, Leah Raj. Advisor: Cheng.
AliciaOptions on Futures, Alicia Van Sciver. Advisor: Cheng.

2009

Mathematically Modeling the Immunological Spread of HIV/AIDS, Jillian Brown. Advisor: Donnay.
Analysis of the Black Scholes Model: An Imperative in Option Pricing, Catherine Durante. Advisor: Cheng.
Fingerprint Compression using Wavelets, Jendra Hayde. Advisor: Cheng.
Valuation of Barrier Options, Amanda Lu. Advisor: Cheng.
Bond Pricing, Melania Macko. Advisor: Cheng.
Climate Changes, Fisheries, and Mathematical Modeling, Hannah Waterhouse. Advisor: Donnay

2008

Geometric and Topological properties of the Mobius Band, Melanie Edwalds. Advisor: Melvin.
Langevin Equations: Modeling Particle Motion and Trail Formation, Dena Feldman.
Analysis of the Black-Scholes Model: A Catalyst for Financial Mathematics, Jody Krieger. Advisor: Cheng.
Helffer-Sjostrand Proof of the Spectral Theorem, Milena Redzic. Advisor: Hughes.

2007

Isospectral Lattices and Quadratic Forms, Katie Haymaker. Advisor: Melvin.
The Mathematical Dissection of Social Networks, Huong Huynj. Advisor: Donnay.
Spectral Theorem for Compact Hermitian Operators, Genevieve Stein O'Brien. Advisor: Kasius.
Intrinsic Linking Numbers of Complete Graphs, Cara Petonic. Advisor: Melvin.
Bounded Mean Oscillation Space, Camille Porreca. Advisor: Cheng.
Thurston-Bennequin Bound of Legendrian Links, Danny Tang. Advisor: Melvin.
Social Network Analysis: Applications to School District Management, Priscilla Won. Advisor: Donnay.

2006

Simplest Cubic Fields and Class Numbers, Nicole Benfold. Advisor: Grundman.
Credit Risk Management, Cindy Do. Advisor: Stromquist.
Stable Solvability of a Family of Quartic Thue Equations, Emily Hammer. Advisor: Grundman.