Senior Theses

May 2023

Alex Burgin

The Schrodinger Maximal Function and Generalizations
Advisor: Lillian Pierce

Nick Chakraborty

Improve Accuracy and Speed of Manifold Reconstruction and De-Noising from Scattered Data in R²
Advisor: Hongkai Zhao

Jeffrey Cheng

Mixing in Measure Preserving Dynamical Systems
Advisor: Tarek Elgindi

Carson Dudley

A Mathematical Model of a Peritoneal Staphylococcus Aureus infection
Advisor: Anna Nelson

Riley Fisher

Pattern Formation in Evolving Domains
Advisor: Tom Witelski

Yijia Liu

Multitaper Wave-Shape F-Test For Detecting Non-Sinusoidal Oscillations
Advisor: Hau-Tieng Wu

Rui Xin

Diffusing on multiple fibers
Advisor: Ingrid Daubechies and Shira Faigenbaum

December 2022

William He

Symmetric Formulas for Products of Permutations
Advisor: Benjamin Rossman

May 2022

Craig Chen

A homotopic variant of policy gradients for the linear quadratic
regulator problem
Advisor: Andrea Agazzi

Nathan Geist

Homological algebra of modules over real polyhedral groups
Advisor: Ezra Miller

Braden Hoagland

Percolation Processes on Dynamically Grown Graphs
Advisor: Rick Durrett

Daniel Hwang

Analyzing the bistability of the minimally bistable ERK network using
the discriminant locus
Advisor: Maggie Regan

Wallace Peaslee

Dolbeault Cohomology of Non-Compact Metric Graphs
Advisor: Joseph Rabinoff

Ethan Wu

Mathematical Modeling of TIE1 and Endothelial Metabolism
Advisor: Michael Reed

December 2021

Norah Tan

Some Mathematical Problems in Quantum Computing and Quantum Information
Advisor: Robert Calderbank

Anuk Dayaprema

Solitons for the closed G2 Laplacian flow in the cohomogeneity-one setting
Advisor: Mark Haskins

Ziyang Ding

At the Intersection of Deep Sequential and State-space Model Framework
Advisor: Sayan Mukherjee

Lucas Fagan

Schur Polynomials and Crystal Graphs
Advisor: Spencer Leslie

Xinchun Hu

Resolving Simpson’s Paradox in NC Public School Grading System
Advisor: Greg Herschlag

Phoebe Klett

Implementing non-canonical Sylvan Resolutions
Advisor: Ezra Miller

Jianyou Wang

Deep Reinforcement Adaptive Computational Processor
Advisor: Vahid Tarokh

Alex Damian

Theoretical Guarantees for Signal Recovery
Advisor: Hau-tieng Wu

Blythe Davis

The Spherical Manifold Realization Problem
Advisor: Faramarz Vafaee

Onkar Gujral

Khovanov Homology and Knot Concordance
dvisor: Adam Levine

Xiayimei Han

Hodge Representations of Calabi-Yau 3 Folds
Advisor: Colleen Robles

Remy Kassem

Symmetry Detection of Unknown Volumes from Projected Variations
Advisor: Xiuyuan Cheng

Joey Li

Algebraic Data Structures for Decomposing Multipersistence Modules
Advisor: Ezra Miller 

Tyler Lian

Evaluating Bayesian Convolutional Neural Networks in the Clinic
Advisor: Paul Bendich

Jonathan Michala

Uniqueness of Ranked Pairs
Advisor: Hubert Bray 

Benjamin Nativi

An Analogue of Gauss Composition for Binary Cubic Forms
Advisor: Aaron Pollack

Sam Pease

Computing Values of Symmetric Square L-Functions using Ichino's Pullback Formula
Advisor: Aaron Pollack

Junmo Ryang

Embedding Lagrangian Surfaces
Advisor: Robert Bryant

Irina Cristali

Poisson Percolation on the Square Lattice
Advisors: Rick Durrett, Matthew Junge

David Geng

Creating Musical Rubato Using Deep Learning
Advisor: Ezra Miller

Zhenhua Liu

Stationary One-Sided Area Minimizing Hypersurfaces with Isolated Singularities
Advisors: William Allard, Hubert Bray, Robert Bryant

Xueying Wang

Unfolding High-Dimensional Convex Polyhedra
Advisor: Ezra Miller

Claire Wiebe

Analyzing the Effects of Partisan Correlation on Election Outcomes using Order Statistics
Advisor: Jonathan Mattingly

Gaitling Zhou

Elliptic Curves over Dedekind Domains
Advisor: William Pardon

(you can search for archived versions of these theses here)

• Surabhi Beriwal Statistical analysis of fruit fly wing vein topology (2018) [with E. Miller]
• Trung Can The Heisenberg-Weyl Group, Finite Symplectic Geometry, and their applications  (2018) [with R. Calderbank]
• Feng Gui On Calibrations for Area Minimizing Cones (2018) with [H. Bray]
• Neel Kurupassery  Cryptographic Primitives in Artin Groups of Type I_k(m)  (2018)  [with M. Abel]
• Eric Peshkin  The quantification of markers of economic development from time-series satellite imagery using deep learning (2018) with [with P. Bendich and D. Thomas]
• Weiyao Wang  Understanding Operator Reed-Muller Codes Through the Weyl Transform (2018) [with R. Calderbank]
• Alexander Pieloch The Topology of Moduli Spaces of Real Algebraic Curves (2017) [with R. Hain]
• Samadwara Reddy The Vietoris–Rips Complexes of Finite Subsets of an Ellipse of Small Eccentricity (2017) [with H. Adams]
• Lindsey Brown An Application of Abstract Algebra to the Neural Code for Sound Localization in Barn Owls (2016) [with M. Reed]
• David Builes The Large Cardinal Hierarchy (2016) [with R. Hodel]
• Kyle Casey Siegel Modular Forms (2016) [with L. Saper]
• Bryan Runjing Liu Modeling the Effects of Positive and Negative Feedback in Kidney Blood Flow Control (2016) [with A. Layton]
• Francois Thelot A Maximum Entropy Based Approach for the Description of
  the Conformational Ensemble of Calmodulin from Paramagnetic NMR (2016)
  [with M. Maggioni and B. Donald]
• Will Victor Efficient algorithms for Traffic Data Analysis (2016)[computer science with P. Agarwal]
• Paul Ziquan Yang Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields (2016) [with C. Schoen]
• Rex Zhitao Ying Approximation Algorithms of Dynamic Time Warping and Edit Distance (2016) [computer science with P. Agarwal]
• Roger Zou Deformable Graph Model for Trackng Epithelial Cell Sheets in Florescence Microscopy (2016)[computer science with C. Tomasi]
• Anne Talkington Modeling the Dynamics of Cancerous Cells in vivo (2015) [with R. Durrett]
• Rowena Gan Geometry of Impressionist Music (2015) [with E. Miller]
• David Hemminger Augmentation Rank of Satellites with Braid Pattern (2015) [with L. Ng and C. Cornwell]
• Mandy Jiang Dynamic random network model for human papilloma virus transmission (2015) [with M. Ryser]
• Hunter Nisonoff Efficient Partition Function Estimatation in Computational Protein Design (2015) [with M. Maggioni]
• Eugene Rabinovich The Conformal Manifold in N=(2,2) SCFTs   (2015)  [physics  with R. Plesser]
• Marshall Ratliff Introducing the Cover tree to Music Information Retrieval (2015) [with P. Bendich]
• Brett Schnobrich Heisenberg-Weyl Group, Subspace Packings, and Image Processing (2015) [with R. Calderbank]
• Christy Vaughn Stochastic Study of Gerrymandering (2015) [with J. Mattingly]
• Aashiq Dheeraj A Stochastic Spatial Model for Tumor Growth (2014) [with R. Durrett]
• Joshua Izzard Rank p² Representations of Semisimple Lie Algebras (2014) [with J. Getz]
• Kathleen Lan Coalescing random walks on n-block Markov chains (2014) [with K. McGoff]
• Leslie Lei Lei Infinite Swapping Simulated Tempering (2014) [with J. Lu]
• Julia Ni A convex approach to tree-based wavelet compression (2014) [with A. Thompson]
• Jiarou Ivy Shen Merge times and hitting times of time-inhomogeneous Markov chains (2014) [with D. Sivakoff]
• Daniel Stern Low-Order Lagrangians Depending on a Metric and a Matter Field of Arbitrary Rank (2014) [with H. Bray]
• Daniel Vitek Knot Contact Homology and the Augmentation Polynomial (2014) [with C. Cornwell]
• Alexander Wertheim Complex Multiplication on Elliptic Curves (2014) [with L. Saper]
• Luxi Wei Modeling Credit Risk using Rating and Environmental Factors (2014) [with R. Durrett]
• Timothy Chang On the existence of a simple winning strategy in the T(4.3) knot game (2013) [with D. Herzog]
• Conrad de Peuter Modeling basketball games as alternating renewal-reward processes and predicting match outcomes (2013) [with R. Durrett]
• Bryan Jacobson A practical approximation of persistent local homology (2013) [with P. Bendich]
• Kara Karpman Simulating mucociliary transport using the method of regularized Stokelets (2013) [with A. Layton]
• Carmen Lopez Modeling the folate pathway in Escherichia coli (2013) [with A. Layton]
• James Mallernee Strategy and honesty based comparison of preferential ballot voting methods (2013) [with H. Bray]
• William Zhang Evolutionary dynamics in host pathogen model (2013) [with R. Durrett]
• Ben Bellis Investigation of a Local Computation of the Signature from the Triangulation of a Manifold (2012) [with M. Stern]
• Adrian Chan Pricing financial derivatives with multi-task machine learning and mixed effects method (2012) [with J. Bouvrie]
• Kyu Won Choi Relative contributions of common jumps in realized correlations (2012) [with A. Petters]
• Veronica Ciocanel Analysis of the nonlinear dynamics of the forced planar string pendulum (2012) [with T. Witelski]
• Kaveh Danesh A branching process model of ovarian cancer (2012) [with R. Durrett]
• Theo Frehlinghuysen Carbon sequestration via forest management techniques (2012) [with D. Kraines]
• Yingyi Shen A study of edge toric ideals using associated graphs (2012) [with S. Mapes]
• Daniel Thielman Complex-balanced steady state of chemical reaction networks that contain an Eulerian cycle (2012) [with C. Berkesch]
• Kaitlin Daniels Noise driven Transitions between stable equilibria in stochastic dynamical systems (2011) [with A. Athreya]
• Alan Guo Lattice point methods for combinatorial games (2011) [with E. Miller]
• Nils Hultgren Centrality and network analysis: A perturbative approach to dynamical importance (2011) [with I. Matic]
• Hans Kist Estimating carbon sequestration potential in the boreal forests (2011) [with D. Kraines]
• Misha Lavrov Invariants in Legendrian links in the solid torus (2011) [with D. Rutherford]
• Philip Pham Tubuloglomerular feedback signal transduction in the loops of Henle (2011) [with A. Layton]
• Thames Sae Sue A simple cardiac model exhibiting stationary discordant alternans (2011) [with D. Schaeffer]
• Max Tabachnik An analysis of preferential ballot voting methods (2011) [with H. Bray]
• Bo Waggoner A model of the foot and ankle in running (2011) [with E. Bouzarth]
• Wutichai Chongchitmate Classification of Legendrian knots and links (2010) [with L. Ng]
• Jason D. Lee Multiscale analysis of dynamic graphs (2010) [with M. Maggioni]
• Jeremy Semko Statistical analysis simulations of coarsening droplets coating a hydrophobic surface (2010) [with T. Witelski]
• Amy Wen Model of feedback-mediated dynamics of coupled nephrons with compliant thick ascending limbs (2010) [with A. Layton]
• Jason Ferguson Factorization of Primes in Biquadratic Extensions of Q (2009) [with C. Schoen]
• Jared Haftel A Closer Look at ADC multivariate GARCH (2009) [with M. Huber]
• Mark Hallen Improving accuracy and scope of quantitative FRAP analysis (2009) [with A. Layton]
• Andy Ng Retinoid Transport in the Vision cycle (2009) [with J. Mercer]
• Aaron Pollack Relations between special derivations arising from modular forms (2009) [with R. Hain]
• Jesse Thorner Simplicial homology and DeRham’s theorem (2009) [with W. Allard]
• Barry Wright III Objective measures of preferential ballot voting systems (2009) [with H. Bray]
• Michael Bauer Existence and stability of patterns arising from square wave forcing of the damped Mathieu equation (2008) [with A. Catlla]
• Tirasan Khandhawit On Legandrean and transverse knots (2008) [with L. Ng]
• Aalok Shah An overview of fast marching and optimal control methods for trajectory optimization (2008) [with W. Allard]
• Charles Staats III Application of discrete geometry to the construction of Laurent-rational zeros (2008) [with S. Sharif]
• Elliott Wolf Computational pathways to Godel’s first incompletness theorem (2008) [with R. Hodel]
• Lingen Zhang The motion of sets of vortices (2008) [with T. Witelski]
• Morgan Brown An algorithm for tracking persistence pairing of a discrete homotopy of Morse functions on S² (2007) [with J.Harer]
• Brandon Levin Class field theory and the problem of representing primes by binary quadratic forms (2007) [with L. Saper]
• Stepan Paul Lines and conics relative to degenerating divisors in CP² (2007) [with J. Davis]
• James Zou 3-D reconstruction and topological analysis of root architecture (2007) [with J. Harer]
• Pradeep Baliga Dynamic cellular automata model of toll plaza traffic flows (2006) [with W. G. Mitchener]
• Adam Chandler Dynamic cellular automata model of toll plaza traffic flows (2006) [with W. G. Mitchener]
• Matthew Fischer Mapping model of cardiac-membrane dynamics (2006) [with D. Schaeffer]
• Qinzheng Tian Simulation of Newtonian fluid flow between rotating cylinders (2006) [with T. Witelski]
• Yee Lok Wong Models of instant runoff voting (2006) [with J. Mattingly]
• Oaz Nir Mechanical arms and algebraic topology (2005) [with J.Harer]
• Mayank Varia Explicit calculation of the L invariant for Kummer surfaces (2005) [with J. Hanke]
• David Arthur On the higher Hasse-Witt matrices and related in variants (2004) [with W. Pardon]
• Suzy Borgschulte A mathematical approach to the panting of dogs (2004) [with M. Reed]
• Lauren M. Childs Scaling population dynamics from the macroscopic to the microscopic (2004) [with T. Kepler]
• Ryan Letchworth Wavelet methods for numerical solutions of differential equations (2004) [with S. Roudenko]
• David Marks Coadjoint orbits and geometric quantization (2004) [with M.R. Plesser]
• Lori Peacock Distributions of the small eigenvalues of Wishart matrices (2004) [with B. Rider]
• Lindsay C. Piechnik Smooth reflexive 4-polytopes have quadratic triangulations (2004) [with C. Haase]
• Matthew Toups A solution to the D0-D4 system of equations (2004) [with M. Stern]
• Jenna VanLiere Mathematically modelling the growth and diversification of T-cell populations (2004) [with T. Kepler]
• Matthew J. Atwood Evaluating singular and nearly singular integrals numerically (2003) [with J.T. Beale]
• Marie Guerraty Controlling alternans in a cardiac map model (2003) [with M. Romeo]
• Meredith C. Houlton Classification of critical curves and preliminary analysis of caustics (2003) [with A. Petters]
• Steven R. Nicklas Envy and satisfaction in the public goods game (2003) [with D. Kraines]
• Dane R. Voris A numerical approach to the M_t/M_t/N_t queue with abandonment (2003) [with B. Rider]
• Melanie Wood Invariants and relations of the action of the absolute Galois group on dessins d’enfants and the algebraic fundamental group of the punctured sphere (2003) [with R. Hain]
• Thomas W. Finley Efficient Myrinet routing (2002) [with W. Allard]
• Samuel W. Malone Alternative Price Processes for Black-Scholes: Empirical Evidence and Theory (2002) [with A. Petters]
• Carl Miller Exponential Iterated Integrals and the Solvable Completion of Fundamental Groups (2001) [with R. Hain]
• Daniel Neill Optimality under Noise: Higher Memory Strategies for the Alternating Prisoner’s Dilemma (2001) Computer Science [with D. Kraines]
• Luis Von Ahn Models of the language of set theory and Zermelo Frankel axioms (2000) [with R. Hodel]
• Christopher Beasley Superconformal theories from Branes at Singularities (1999) Physics [with R. Plesser]
• Alexander Brodie Measurable Cardinals (1999) [with R. Hodel]
• Jeffrey DiLisi The Biology and Mathematics of the Hypothalamic-Pituitary-Testicular Axis (1999) [with M. Reed]
• Garrett Mitchener Lattices and Sphere Packing (1999) [with R. Hain]
• Andrew O. Dittmer Generalized Formulas for Circular Polygons (1998) [with R. Hain]
• Richard R. Schneck Set Theory and Cardinal Arithmetic (1997) [with R. Hodel]
• Tung T. Tran Counting Independent Subsets in Nearly Regular Graphs (1997) [with G. Lawler]
• Paul A. Dreyer Knot theory and the human pretzel game (1995) [with J. Harer]
• Paul J. Koss Effects of noise on the iterated prisoner’s dilemma (1995) [with D. Kraines]
• Jeff Vanderkam Eigenfunctions of an acoustic system (1994) [with T. Beale]
• Linie Chang Mathematics and immunology: Modeling antigen and antibody interactions (1993) [with M. Reed]
• Sang H. Chin Action of the Torelli group on the 3-fold cover of G-hole torus (1993) [with R. Hain]
• Jennifer Slimowitz Transitions of gaps between the integers N satisfying Nq < j (1993) [with M. Reed]
• David Jones Primality testing, factoring and continued fractions (1992) [with C. Schoen]
• Will Schneeberger The axiom diamond (1992) [with J. Shoenfield]
• Jeanne Nielsen Triply periodic minimal surfaces in R³ (1991) [with R. Bryant