Students who write theses in mathematics spend an entire academic year working on an in-depth study with the help and direction of a faculty member. In addition to writing a thesis, each student gives a seminar late in spring semester. The thesis seminar weeks are busy and exciting times around the department.

Copies of some past student theses are located in the Seeley Mudd library.

### 2024

**Leo Xu**worked with Prof. Aamir Rasheed on "Classifying Abelian Fundamental Groups of Three-Manifolds""**Phillip Zhou**worked with Prof. Ryan Alvarado on "The Ins and Outs of Optimal Transport"**Leandro Arcos Román**worked with Prof. Ivan Contreras on "The Graph Laplacian and Discrete Morse Theory (Can We Hear the Shape of a Graph?)"**Wenche Tseng**worked with Prof. Greg Call on "The Algebraic Number Theory of the Ideal Class Pairing"**Kathy Xing**worked with Prof. Amanda Folsom on "Traces of Singular Moduli as the Coefficients of a Meromorphic Modular Form"**Michael Liu**worked with Prof. Nathan Pflueger "Subsystem Codes: Structure and Correctability"**Ally Deegan**worked with Prof. Kate Moore "K-Clustering with Cohesion"**Alan Li**worked with Prof. David Zureick-Brown "Greatest Hits of Ramsey Theory"

### 2023

**William DeGroot**worked with Prof. Harris Daniels on "Obstructions to Galois Embedding Problems"**Thomas Meyer**worked with Prof. Amanda Folsom on "Resolution of the Alder-Andrews Conjecture"**Keane Ng**worked with Prof. Michael Ching on "Morse Theory and Homology"**Ethan Spingarn**worked with Prof. Emeritus David Cox on "Affine Kac-Moody Lie Algebras, Vertex Algebras, and Moonshine"**Zachary Steinberg**worked with Prof. Amalia Culiuc on "How to Fool One and a Half Supermen"**Min Winton**worked with Prof. Ivan Contreras "On The Classification of Irreducible Representations of SU(2)"

### 2022

**Anna Dietrich**worked with Prof. Rob Benedetto on "Iteration of Rational Functions with Colliding Critical Points"**Leah Johnson**worked with Prof. Greg Call on "Elliptic Curves and the Ideal Class Pairing"**Sophie Launsbach**worked with Prof. Sema Gunturkun on "Neural Codes and Neural Rings"**Holden Lee**worked with Prof. Harris Daniels on "Identifying Complement Subgroups in Finite Group Extensions"**Elizabeth (Baz) Pratt**worked with Prof. Jenia Tevelev (UMass) on "On The Geometry of Elliptic Pairs"**Audrey Rosevear**worked with Prof. Weimin Chen (UMass) on "Taut Foliations and Minimal Genus Surfaces in 3 and 4 Dimensions"**Amaya Smole**worked with Prof. Tanya Leise on "A Network Model for COVID-19"**Noah Solomon**worked with Professor Nathan Pflueger on "Chip-Firing on Twice-Marked Graphs of Genus 2"

### 2021

**Jonah Botvinick-Greenhouse**worked with Prof. Ryan Alvarado on "An Introduction to the Theory of the Ergodic Partition"**Lianbi Ji**worked with Prof. Greg Call on "Torsion Subgroups of Elliptic Curves over Q and over Quadratic Number Fields"**Yuuna Klindziuk**worked with Prof. Kara Yacoubou Djima on "Fourier Analysis on Graphs"**Emily Minus**worked with Prof. Tanya Leise on "A Compartmental Model of COVID-19"**Andrew Tawfeek**worked with Prof. Ivan Contreras on "Discrete Morse Theory: Enumeration of Discrete Gradient Vector Fields"**Justin Warring**worked with Prof. Amanda Folsom on "On 'Strange' Identities and Quantum Modular Forms: q-hypergeometric Identities and Modular Properties of a Peculiar Function due to Kontsevich"**Calvin Woods**worked with Prof. Amalia Culiuc on "Lp Weighted Estimates and Matrix Weights"

### 2020

**Gregory Carroll**worked with Prof. Robert Benedetto on "Prolegomenon to Hrushovski's Stabilizer Theorem"**Cameron Chandler**worked with Prof. Nathan Pflueger on "Riemann-Roch and Displacement on Chains of Cycles"**Sai Chauhan**worked with Prof. Yongheng Zhang on "Introduction to the Kontsevich Integral"**Max Fox-Jurkowitz**worked with Prof. Ryan Alvarado on "Set Representation Using Convex Analysis"**Joseph Lupo**worked with Prof. Robert Benedetto on "Dynamical Galois Groups, Monodromy Groups, and Three Galois Correspondences"**Alexander Mangiafico**worked with Prof. Ivan Contreras on "Persistent Homology in Topological Data Analysis"**Shashank Sule**worked with Prof. Karamatou Yacoubou Djima on "Two Multiresolution Frameworks on Graphs"

### 2019

**Katherine Finnerty**worked with Prof. Harris Daniels on "Representability of Primes as Sums of Squares An Introduction to Class Field Theory"**Caroline MacGillivray**worked with Prof. Gregory Call on "Binary Quadratic Forms and the Class Group"**Ellie Thieu**worked with Prof. David Cox on "The Riemann-Roch Theorem: Analytic and Algebraic"

### 2018

**Michael Barnett**worked with Prof. Robert Benedetto on “Modular and Jacobi Forms”**Jennifer Cain**worked with Prof. Gabriel Sosa on “Detecting Normal Toric Rings Using Gröbner Bases”**Lily Fang**worked with Prof. Jamie Juul on “An Arboreal Galois Group of a PCF Quadratic Polynomial”**Seong Eun Jung**worked with Prof. Harris Daniels on “Galois Representations Associated to Torsion Points of Elliptic Curves”**Nathanael Lane**worked with Prof. David Cox on “Stewart-Gough Kinematics and Homotopy Continuation**Fernando Liu Lopez**worked with Prof. Yusra Naqvi on “Coxeter Groups from a Combinatorial and Geometric Perspective”**Obinna Ukogu**worked with Prof. Tanya Leise on “Using Queueing Theory to Model Enzyme-Substrate Interactions”**William Wesley**worked with Prof. Amanda Folsom on “Combinatorial Proofs of Ramanujan’s Congruences”**Bowen Yang**worked with Prof. Gregory Call on “Mordell’s Conjecture Canonical Heights and Vojta’s Inequality”**Hui Xu**worked with Prof. Yao Li (UMass, Amherst) and Prof. Gregory Call on “Comparison of Stochastic Neural Field Models with Corresponding Mean-field Approximations.

### 2017

**Fraser Binns**worked with Prof. Michael Ching on "The Kervaire Invariant of the Lie-framed Torus"**Felipe Pereira Debayle**worked with Prof. David Cox on "Interactions between Commutative Algebra, Galois Theory, and Representation Theory"**Paul Gramieri**worked with Prof. Rob Benedetto on "Applications of Sieve Methods"**Caleb Ki**worked with Prof. Nick Horton on "Handling Missing Data in Randomized Clinical Trials"**Levi Lee**worked with Prof. Amy Wagaman on "A Simulation Study Using Graph Models to Fit Social Networks"**Emily Masten**worked with Prof. Gabriel Sosa on "Matroid Theory and Its Application to Combinatorial Optimization"**Jacob Pfau**worked with Prof. Yusra Naqvi on "Algebraic and Topological properties of Graph Products"**Yen Nhi Truong Vu**worked with Prof. Amanda Folsom on "On the Modular Transformations and Asymptotic Behaviors of Mock Modular Forms"

### 2016

**Becky Danning**worked with Prof. Tanya Leise on "Measuring Centrality in Undirected Valued Networks"

**Kyle Ferendo**worked with Prof. Michael Ching on "The Maximal and Free (∞,n)-Categories of an (∞,n+1)-Category"**Hannah Goodwillie**worked with Prof. Harris Daniels on "The Ranks of Elliptic Curves with n-isogenies"**Cole Hawkins**worked with Prof. David Cox on "Boij-Soderberg Theory on Particular Classes of Modules"

### 2015

**Dvij Bajpai**worked with Prof. Dan Velleman on “Topological Predictors and*T*-Anonymous Predictors in Hat Problems”**Kush Chandra**worked with Prof. Greg Call on “The Elliptic Curve Discrete Logarithm Problem and the Weil Pairing”**Stephen Hetterich**worked with Prof. Rob Benedetto on “The Group of Rational Points on Elliptic Curves”**Namyi Kang**worked with Prof. Tanya Leise on “A Comparison of Mathematical Models of Decision Making Using Eye Tracking Analysis”**Edward Kim**worked with Prof. Amanda Folsom on “An Application of the circle Method in Analytic Number Theory to the Partition Function”**Sage O’Neil**worked with Prof. David Cox on “Group Representations and Applications to Chemistry”**Darius Onul**worked with Prof. Amy Wagaman on “Using Hidden Markov Models to Predict Stock Pricing”**Lucia Minah Yang**worked with Prof. Jacqueline Dresch on “An Investigation of Numerical Methods of Solving Linear Problems (Ax=b)”

### 2014

**Ruqian Chen**worked with Prof. David Cox on “Classification of transitive solvable imprimitive subgroups of symmetric groups of prime squared degrees”**Alexander W. Diones**worked with Prof. James Henle (Smith College) and Prof. Dan Velleman on “Forcing over Partial Models of ZFC: The Independence of the Continuum Hypothesis”**Shanghui Li**worked with Prof. Tanya Leise on “Application of Wavelet Methods in the Analysis of Rhythmic Activity and Coupling Relationships in the Suprachiasmatic Nucleus”**Yang Xiao**worked with Prof. Michael Ching and Prof. Rob Benedetto on “1-2 Quadruples in Self-Similar Unbounded Apollonian Circle Packings”

### 2013

**Andrew Erskine**worked with Prof. David Cox on "Binomial Edge Ideals and the Characterization of Closed Graphs"**Anya Goldberg**worked with Prof. Robert Benedetto on "The Hasse-Minkowski Theorem on Quadratic Forms"**Taylor Grant-Knight**worked with Prof. Daniel Velleman on "Categorizing Computability: A Study of Recursively Enumerable Degrees"**R. Henry Weaver**worked with Prof. Daniel Velleman on "Elusive Points: Topics in Constructive Analysis"**David (Hao) Zhang**worked with Prof. Amy Wagaman on "Compositional Data Analysis"

### 2012

**Trevor Hyde**worked with Prof. David Cox on "Dividing the Lemniscate An interplay of elliptic functions, class field theory, and complex multiplication"**Brian Kim**worked with Prof. Shu-Min Liao and Prof. Daeyoung Kim (UMass) on "Perfect Pitch: An analysis of Pitchers Using Pitch F/X Data"**Ariah Klages-Mundt**worked with Prof. Robert Benedetto and Prof. Paul Gunnells (UMass) on "Computing Elliptic Curves over Complex Cubic Fields"**Yordanka Kovacheva**worked with Prof. Robert Benedetto on "Serre Duality"**Dang Trinh**worked with Prof. Tanya Leise on "Stock Volatilities: Long Memory and Common Factors"

### 2011

**Adam Humphries**worked with Prof. Velleman on "ρ-GAP*q*-CSP is NP-hard"**Samuel Smith**worked with Prof. R. Benedetto on "Measure-Theoretic Entropy, Topological Entropy, and the Variational Principle"

### 2010

**Ben Krause**worked with Prof. Cox on "Plane Curves and their Singularities"**Michael Kreisel**worked with Prof. Cox of Amherst and Prof. Rob Kusner (UMass) on "A Classification of Euclidean Surfaces with Conical Singularities"**Sam Schiavone**worked with Prof. Leise on "Cloaking and Invisibility By Change Of Variables"**Andrey T. Tagarev**worked with Prof. Leise on "Speech Recognition with Artificial Neural Networks"

### 2009

**Maya Miller-Vedam**worked with Prof. Benedetto on "The Riemann Hypothesis for Curves Over Finite Fields"**Stephen O. Oloo**worked with Prof. Cox on "The Gelfand Representation of Unital Commutative Banach Algebras"

### 2008

**Benjamin Dickman**worked with Prof. Benedetto on "On a Theorem of Dwork"**Sasha E. Joseph**worked with Prof. Benedetto on "Algebraic Number Theory and Density Theorems"**Jeremy Newton**worked with Prof. Tranbarger on "Prototype Patterns of a Poisson Process"**Gina Turrini**worked with Prof. Tranbarger on "Sex and Statistics: A Bootstrap Study Using Multiple Logistic Regressions Modeling and Odds Ratios to Explore Sexual Attitudes and Behaviors in the National Survey of Family Growth"**Austin Yim**worked with Professor Velleman on "Relevance Logic and Relevant Arithmetic"

### 2007

**Sarah G. Cotter**worked with Prof. Velleman and Prof. Jim Henle (Smith College) on "Elementary Embeddings and Left-Distributive Algebras"**Benjamin Purkis**worked with Prof. Cox on "Ergodic Theory and Continued Fractions"

### 2006

**Tsvetelina V. Petkova**worked with Prof. Starr and Prof. Ruth Haas (Smith College) on "Nonisomorphic Graph Colorings"

### 2005

**Wing L. Mui**worked with Prof. Cox on "An Introduction to Polynomial Knots"**Mathew A. Wechter**worked with Prof. Starr on "An Analytic Proff of the Prime Number Theorem"

### 2004

**Mihailis E. Diamantis**worked with Prof. Velleman on "The Independence of the Continuum Hypothesis"**Andrew K. Gilette**worked with Prof. Benedetto on "Searching for Small Canonical Heights: Finding A Minimum Speed Limit On the Road to Infinity"**Adam M. Lowrance**worked with Prof. David Cox on "Solutions of Equations over Finite Fields"**Paul Reschke**worked with Prof. Benedetto on "Rational Periodic and Preperiodic Points of Polynomial Functions"

### 2003

**Richard P. Laurberg**worked with Prof. Call on "A Primer on the Birch-Swinnerton-Dyer Conjecture"**Michael A. Stevens**worked with Prof. Call on "The Ideal Class Pairing on Elliptic Curves"

### 2002

**Brian Carty**worked with Prof. Velleman on "Non-Standard Times Call for Non-Standard Analysis: An Introduction to Infinitesimal Reasoning"

### 2001

**William E. Gryc**worked with Prof. Cox on "Wavelets and Multiresolution Analysis"**Anushka Krishnachander**worked with Prof. Velleman on "An Introduction to Combinatorial Game Theory and the Game of Hackenbush"

### 2000

**James D. Hunter**worked with Prof. Velleman on "On the Structure of the Recursively Enumerable Degrees"**Thomas B. Wexler**worked with Prof. Starr and Prof. Haas (Smith College) on "Some Results on Signed Domination in Graphs"

### 1999

**David S. Spiegel**worked with Prof. Cox on "Symmetries of the Helmholtz Equation"

### 1998

**Ben Brubaker**worked with Prof. Cox on "An Investigation of Singularities of the Evolute"**Dan Golosovker**worked with Prof. Call on "Preperiodic Points of Polynomials in Number Fields"**Spencer Hamblen**worked with Prof. Call on "Calculating the Circle Pairing over Families of Elliptic Points"**Chris Hardin**worked with Prof. Velleman on "Reverse Mathematics and the Mean Value Theorem"**Raphael Jones**worked with Prof. Armacost on "The Frattini Subgroup"

### 1997

**Chris Hale**worked with Prof. Call on "Preperiodic Points of Morphisms over Function Fields"

### 1996

**Lawrence Snyder**worked with Prof. Starr and Prof. Haas (Smith College) on "Combinatorial Rigidity and the Path Decomposition of Isostatic Graphs"**Michael Stanfield**worked with Prof. Cox on "Polynomial Equations and Abstract Algebra"**William Wasik**worked with Prof. Velleman on "The Suslin Problem and Whitehead's Problem are Undecidable"