Student Research

2019

• Kate Blaine: Determinantal Conditions on Integer Splines
• Chenyu Chang: Investigations of finding all stable solutions of Stable Marriage Problem
• Corey Chang: Markov Chains in Music Composition
• Danielle Degutz: Gerrymandering and the Impossibility of Fair Districting Systems
• Jintao Fang: The Credit Scorecard Model
• Jazlyn Johnson: An Algorithmic Approach to Detect Non-injectivity of the Partial Borda Count
• Meagan Kenney: The Conditional Probability That an Elliptic Curve Has a Rational Subgroup of Order 5 or 7
• Leah Leiner: Polygonal Analogues to Topological Tverberg-type and van Kampen-Flores-type Theorems
• Shenze Li: Upper Bounds for the Number of Lattice Edges Needed to Represent 4-Regular Graphs as Lattice Graphs
• Yushi Pan: From Black-Scholes Model to Pricing Models of American Options: A Performance Comparison
• Eliot Roske: Analyzing Flow Free with One Pair of Dots
• Maya Schwartz: Factorization Lengths in Numerical Monoids
• Edward Skorupa: Time and Finance: An Exploration of Variance in the Black-Scholes Model
• Ari Spiesberger: Supersymmetry and the Math of Adinkras
• Sofia Thompson: Econometric Methods for Comparative Case Studies: Lessons From the Dominican Prison Reform
• Rao Vinnakota: Predicting How People Vote from How They Tweet
• Jade Waring: A Strength Test for the Borda Count
• Hsin-Fang Wu: From Constant to Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models
• Alexis Hao Zheng: Happy Numbers in Iterations of Degree 3

2018

• Samuel Baumgartner: Hamilton Paths in the Game of Flow
• Teagan DeCusatis: Analyzing the Probabilistic Spread of a Virus on Various Networks
• Yuan Jessica Liu: Graph Replacement Systems for Julia Sets of Quadratic Polynomials
• Yuming Liu: Stock Price Forecasting Using Stochastic Processes and Machine Learning
• Andres Mejia: Applications of Equivariant Topology In Cascading Makeev Problems
• Avery Morris: From Random to Organized: The Architecture of Neural Networks During Development
• Rachel Nalecz: An Implementation of the Solution to the Conjugacy Problem on Thompson's Group V
• Nguyen Thuy Linh: Expected Value and Standard Deviation of the Center of Mass of Random Configurations
• Odett Salcedo: Ties in Ranked Voting Systems
• Peter Servatius: Concerning the Construction of Fourbar Linkages and Their Topological Configuration-Spaces
• Kirill Shakhnovskiy: Centroidal Voronoi Tessellations with Few Generator Points
• Yida Shao: Counting Trees in Ladder Graphs
• Kaylynn Tran: Exploring Sequences of Tournament Graphs with Draws
• Christian Yost: Time and Frequency Independent Manipulation of Audio in Real Time
• Jialin Zhang: Hyperplanes Equipartition with Cascading Makeev Condition
• Lingxin Zhao: A Stochastic Mass Function on the Edges of a Graph

2017

• Victoria Chayes: Maximal Quantum Effects Outside A Spinning Black Hole: An Exploration Of The Kerr Metric
• Sarah Ghandour: Random Walks on Thomson’s Group F
• Adrian Gillerman: Equipartitions Using Finite Fourier Analysis
• Christopher Hawke: Quantifying the Affect of The Shift in Major League Baseball
• Sadiki Lewis: Exploring Tournament Graphs and Their Win Sequences
• Finnegan Muller-Hardy: The Expectation for the Center of Mass of Finite Interger Grids
• Justin Shin: Envy-Free Fair Division With Two Players and Multiple Cakes
• Stefan Stojanov: An Alternative Formulation for Nonnegative Matrix Factorization
• Olivia Williams: Modeling Purple Sea Urchin and California Sheephead Populations in Channel Islands Kelp Forests

2016

• Margaret Allardice: Orthogonal Projections of Lattice Stick Knots
• Samuel Audino: Associativity of Binary Operations on the Real Numbers
• Taylor Boone: Abstractions and Analyses of Grid Games
• Alexander Goodlad: Proof Theory: The Meta-Meta Framework of Mathematics
• Christopher Gunnell: The Schur Factorization Property as it Applies to Subsets of the General Laguerre Polynomials
• Cyril Kuhns: Public Key Cryptography with the Brin-Thompson Group 2V
• Emmet Mahdavi: Integer Generalized Splines on the Diamond Graph
• Najee McFarland-Drye: Winning Strategies in The Board Game
• Eliana Miller: A binary integer programming approach for counting KenKen puzzles
• Benjamin Moss: The Facilitation of Sound Waves Using Mathematical and Scientific Methods of Digital Signal Processing
• Xiangying Shuai: Radical Recognition in Off-Line Handwritten Chinese Characters Using Non-Negative Matrix Factorization
• Ningning Song: A Variational Approach to the Moving Sofa Problem
• Zexi Song: Cutoff for Lamplighter Markov Chains on Prisms
• Erin Stuckenbruck: Selecting the Average Alternative: Lose Big, Win Big, and Sum Big
• Polina Vulakh: McKay Graphs and Modular Representation Theory

2015

• Emily Conant: Construction of a Nuclear Shell Model
• Galen Dorpalen-Barry: Rational Tilings of the Unit Square
• Rylan Gajek-Leonard: Irreducibility and Galois Properties of Lifts of Supersingular Polynomials
• Ester Gjoni: Basis Criteria for n-cycle Integer Splines
• Andy Huynh: Geometry of adinkra embeddings
• Mohd Ahnaf Khan: Pre-processing for K-means Clustering Algorithm
• Christiane Koffi: Exploring a Generalized Partial Borda Count Voting System
• Erik Lovece: Extending the Planar Voronoi Nets of a Set of 6 Sites to Planar Voronoi Nets of a Set of 7 Sites
• Sharma Maharaj: Resistance on Infinite Networks
• Van Mai Nguyen Thi: Development and Optimization of a Two-View Model for Anamorphic Projections on Planar Surfaces
• Joanna Regan: Inferring Connectivity of Neural Networks during Collision Avoidance in Xenopus Tadpoles
• Jake Weissman: Modeling Stochastic Traps: The Evolution of Preference in a Temporally Heterogeneous Ecological Trap
• Shuyi Weng: Homeomorphism Groups of Fractals
• Noah Winslow: On the Realizability and Rigidity of Graphs in Higher Dimensions
• Xingye Zhang: Aye or Nay: A Study of Opinion Exchange Dynamics

2014

• Siddhartha Baral: Investigating Occupancy Using Maximum Likelihood Estimation
• Celeste Cass: Robots Switching Positions on Graphs
• Zena Coles: Counting Points on Conics Over Finite Fields
• Carlos Gadelha: Option Pricing Model on the Discrete World
• Yushan Jiang: The Analysis of Probabilistic Spread on Complete Graphs
• Benjamin Kane: The Probabilistic Spread of a Virus on a Network
• Lara Merling: Fighting Fires on Semi-Regular Tesselations
• Rajasri Narasimhan: Voter Empowerment and an Exploration of Partial Borda Count
• Linh Pham: From String Theory to Elliptic Curves over Finite Field Fp
• Page Redding: Deformations of Conic Sections
• Carmen Rodriguez: Graphical Model for Three-Way Living Donor Kidney Exchange
• Nicole Rosato: Fire Containment on Layered In nite Grids
• Kimberly Sargeant: A Dinner for Two: Winning the Ethiopian Dinner Game

2013

• Ian Barnett: Mod 2 Homology of Posets
• Abhinanda Bhattacharyya: Forbidden Minors for a Pursuit Game on Graphs
• Lara Bradford: Enumerating Chains for Partially Ordered Sets
• Emily Carlson: A model of Charge Transport in a Dye-Sensitized Solar Cell
• Fiona Do Thi: The Firefighter Problem on Grids: Resistant Networks
• Joe Foy: Inscribed Squares in Taxicab Polygons
• Nabil Hossain: Implementation of the Solution to the Conjugacy Problem in Thompson's Groups
• Matt Hughes: Galois Representations from Non-Torsion Points on Elliptic Curves
• Ruth Lakew: Gaussian Primes Path to Infinity
• Weiying Liu: Distribution of Prime Numbers in Short Intervals
• Iliana Maifeld-Carucci: Designing DNA Nanostructures: Optimization of Tetrahedra Stellation
• Anam Nasim: Spread of a Virus on Networks: A Probabiistic Approach
• Mark Neznansky: Supersymmetry and Non-Relativistic Quantum Mechanics
• Jeff Pereira: "SuperSET," a mathematical investigation of a variation of SET
• Anisha Ramnani: Explorations of the Shannon Switching Game
• Joy Sebseta: Bard Bipartite Sprouts!
• Will Smith: Thompson-Like Groups for Dendrite Julia Sets
• Jacqueline Villers: Counting the Votes: Exploring a Partially Ordered Borda Count
• Jasper Weinrich-Burd: A Thompson-Like Group for the Bubble Bath Julia Set
• Layla Wolfgang: Sets of Splines with Boundary Conditions
• Fanny Wyrick-Flax: Algebraic Relations and Boij-Söderberg Theory

2012

• Jeannette Benham: Auditory Perception in Flatland: The Physical Applicability of a Two-Dimensional Cochlear Model
• Ke Cai: Supersymmetric Gauge Theory
• Siyao Du: A Linear Algebraic Approach to Information Retrieval
• Adriana Johnson: Optimal Control of Cell-Cycle-Specific Chemotherapy: An Examination of the Effects of Necrosis
• Yunxia Jia: Sprouts Game Study
• Sankapla Khadka: Quantum Codes and Computation
• Youseung Kim: Micropatterning of Chemical Oscillation Reactions
• Stergios Mentesidis: Welfare versus Stability in “Stabilizing an Unstable Economy”: A Minskyan Growth Model
• Mariya Mitkova: Squares on Lattices: an Investigation Inspired by the Square Peg Problem
• Lindsey Scoppetta: Modules of Splines with Boundary Conditions
• Evan Seitchik: Trend and Detail: Gap Filling with the Empirical Mode Decomposition
• Zana Tran: A Module-Theoretic Approach to Supersymmetric Gauge Theory
• Kimberly Wood: Switching the Shannon Switching Game
• Zhiwei Wu: Computable Invariants for Quandles
• Dimin Xu: Extrapolation and Correlation Using the Empirical Mode Decomposition: An Application to Economic Time Series
• Yuan Xu
• Yongqing Yuan: The Collision Regions Between Two Epidemic Models: SIR vs. SEIR
• Changwei Zhou: Bases for representation rings of Lie groups and their maximal tori

2011

• Lionel Barrow: A Method for Automatically Generating Network Structure in Bayesian Classifiers
• Julia Bennet: Filtering Irreducible Clifford Supermodules
• Lexi Carver: Generically Rigid Bar Frameworks in Three Dimensions
• Adam Chodoff: Twisted Three-Eared Rabbits: Identifying Topological Quadratics Up To Thurston Equivalence
• Anastassia Etropolski: Specializations of Jacobi polynomials and their algebraic properties
• Alex Fragkopoulos: Electron Scattering in Crossed Electric and Magnetic Fields: A Semiclassical Study
• Diana Khaburzaniya: 
• Travis McGrath: Elliptic Curves: Minimally Spanning Prime Fields and Supersingularity
• Jules Moreau: The Mathematics of Change Ringing
• Madeline Schatzberg: Classifying Derived Voltage Graphs
• Ben Selfridge: Characters of Combinatorial Hopf Algebras
• Nathan Smith: Non-Commutative Linear Algebra
• Jackie Stone: Generalized Adinkra Homology
• Zhexiu Tu: Square Peg Problem on Lattice Plane

2010

• Wui Ming Aldrich-Gan: The Art of Retargeting (or Retargeting of Art): Fitting a Rectangular Peg Into a Square Hole
• Aleksandar Chakarov:
• Cedric Cogell:
• Sarah Farell: Classifying Frequencies of Various Drumheads
• Jonathan Fivelsdal: Simulating Global Climate Using A Simple Model
• Elias Halloran: Mathematical Implementations: Modeling Folds in a Real Coordinate Space
• Xian He: Standing Wave Analysis
• Liz A. Jiminez-Martinez: Enumerating faces of Zonohedra
• Huaizhou Jin: Mapping and Localization on Graphs with Particle Filter Algorithm
• Shun-Yang Lee: Time-Frequency Analysis of the Shepard Tone
• Paul McLaughlin: Chaos in Bird Vocalizations
• Samantha Alison Mutter: Happy Numbers: An Exploration of An Iterated Function in Different Bases
• David Polett: Empowering the Voter: A Mathematical Analysis of Borda Count Elections with Non-Linear Preferences
• Hannah Quay-de la Vallee: Term Rewriting Systems and Their Corresponding Algebraic Theories
• Viriya Ratanasangpunth: Clifford Codes
• Che Ruisi-Besares: Voronoi Diagrams with Non-Linear Bisectors
• Fang Song: The Impact of China's Unbalanced Sex Ratio on Pre-Marital Education
• Alexandru Vladoi: Wireless networks: A labeling problem
• Xinyuan Xu: Whether and When to Purchase an Annuity in China

2009

• Scott McMillen: The Indescribable Awesomeness of Vertex Colorings
• Mona Merling: A Structure Theorem for Plesken Lie Algebras over Finite Fields
• Nicholas Michaud: A Three-Element Generating Set for Thompson's Group F
• Sylvia Naples: Classification of Adinkra Graphs
• Anh Pham: The Effect of Income Inequality and Residential Segregation on Infectious Diseases Transmission (joint with Economics)
• Tomasz Przytycki: A Generalization of Restricted n-Rotors from Knots to Graphs
• Serena Randolph: Making Music Visible: The Mathematics behind Chladni Patterns
• Faqir Usman: Using Graphs to Model the Spread and Containment of Fire
• Ezra Winston: Modeling Origami Folding with Thick Paper
• Tina Zhang: Cops and Robbers
• Dexin Zhou: All About Risk
• Zhechao Zhou: Analysis of Heterogeneous Patterns and Social Dynamics in Human Communication (joint with Physics)

2008

• Zachary Hamaker: Clifford Algebra Representations
• Andrija Perunicic: Group Structure of Elliptic Curves over Finite Fields
• Shelley Stahl: Flag h-Vectors of Distributive Lattices

2007

• Robert Feinsinger: Enumerating Lattice Paths that Avoid Forbidden Patterns
• Jordan Volz:

2006

• Michael Knight: Primus: Patterns Primes Produce Plugged into the Expanding Product of a Particular Polynomial
• Benjamin Rin: The Model Theory of Topoi
• Kenneth Ober: Topological Logics

2000–2005

2005

• David Eisenstadter: Perfect Coloring of Periodic Patterns with Translation Groups
• Alina Marinova: Robots' Motion on a Graph: Configuration Spaces for a 2-Robot System
• Janeta Marinova: Closure Operators on Lattices and Boolean Algebras
• Mariana Raykova: Sequential Dynamical Systems

2004

• Rubaba Ali: Application of Grobner Bases to the M-Color Problem for Graphs
• Catherine Belin: Chip-Firing Games
• Kerri-Ann Norton: The Game of Life on a Torus
• Benjamin Rubenstein: Voronoi Tessellations
• Kathryn Smith: Arrays, Rook Circuits, and Mininal Hamiltonian Graphs

2003

• Monica Elkinton: Manipulating Voting Systems: Can We Get There from Hare?
• Elena Grigorescu: Hilbert Series and Free Resolutions
• Jill Patterson: Male of Female? The Application of Fuzzy Logic to Simulate a Bard Student's Decision-Making Process When Determining an Individual's Sex?

2002

• Imran Ahmed: Does the Out Degree of a Vertex Double When an Oriented Graph is Squared?
• Sean Callanan: Combining Isometric Subgraphs of Hypercubes
• Tim Goldberg: Combinatorial Laplacians of Simplicial Complexes
• Lava Yadav: Chromatic Number of Competition Graphs of Top Split Graphs
• Jaren Smith: Hilbert Sequences of Monomial Ideals

2001

• Luke Nickerson:

2000

• Erin Boyer: Forbidden Subgraphs for Edge Domination
• Shankar Gopalakrishnan: Cutting out the Junk: Breaking up Surfaces with Isolated Singularities
• Maren Holmen: SET Theory

1995–1999

1999

• Josh Foure: Speed III : Stop that Bus
• Corina Tanasa: Geodesics Types of Singular Surfaces

1998

• Nathan Ryan: Characterising low dimensional simplicial complexes or playing with kids' toys

1997

• Brant Jones: Conducting a Tabu Search on the Graph Coloring Problem
• Esteban Rubens: Partially ordered sets, generalized fences and dimension
• Rodney Waldhoff: The matching model for routing permutations on graphs
• Brandon Weber: Uniform approximation of continuous functions using artificial neural networks

1996

• Marissa K. Bernstein: Traversability problems in graph theory
• Dan C. Carroll: Smooth surfaces for computer aided geometric design
• He Jiang: Transformations of regular polygons
• Van Anh Nguyen: A binomial model for option pricing
• Joshua Richman: Three is the loneliest number
• Kathryn Ryan: Error-detecting codes via group theory

1995

• Jason Foulkes: Set Product vs. Coset Product
• Nil Ozel: List, and list T-Coloring results for 2-chromatic graphs
• Diego Socolinsky: On the curvature of polyhedra

1990–1994

1994

• Robert Cutler: Edge Domination of G x Qn
• Weili Wu: The classification of discrete patterns, monohedral tilings and some thoughts about k-anisohedral tiles

1993

• Matthew Lee: Counting the subgroups of the dihedral groups : a numerical theoretic approach to abstract algebra
• Thomas Regner: The significance of neural networks for artificial intelligence

1992

• Jeffrey Bolden: Dimension and planarity in partial ordered sets
• Melissa Cahoon: A Graphic analysis of the hare voting system
• David Steinberg: Real and complex etheral calculus : or, playing around with these numbers and seeing what works
• Anne Willig: Three-colorings of cyclic groups

1990

• Jade Bingham: Efficient orientations of city street graphs
• Linda Burgess: Stress Analysis of Axisymmetric Shells
• Laura Muller: Symmetry groups, perfect colorings, and compound designs : staying within the (guide) lines