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The following PhD theses abstracts are available in .pdf format. To see where these students have taken jobs, see the list of recent graduates.

**2023**- Jones Polynomial Obstructions for Positivity of Knots - Lizzie Buchanan
- Triangular Modular Curves of Low Genus and Geometric Quadrati Chabauty - Juanita Duque-Rosero
- Brill-Noether theory via
*K3*Surfaces - Richard Haburcak - Counting Elliptic Curves with a Cyclic
*m*-isogeny over $\mathbb{Q}$ - Grant Molnar - A Diagram-like Basis for the Multiset Partition Algebra - Alexander Wilson
**2022**- On the Thom Isomorphism for Groupoid-Equivariant Representable K-theory - Zachary Garvey
- Evolutionary Dynamics of Collective Action Problems - Matthew Jones
- On Grid Homology for Lens Space Links - Samuel Tripp
- Spectral sequences and Khovanov homology - Zachary Winkeler
- Sequential Image Recovery from Noisy and Under-sampled Fourier Data - Yao Xiao
**2021**- Evolutionary Dynamics of Human Cooperation Across Scales: Dyads, Networks, and Populations - Xingru Chen
- Mathematical modeling of the human circadian rhythms through wearable devices - Yitong Huang
- Bordered Floer homology over $\mathbb Z$ - Douglas Knowles
- Optimization, Statistical Inverse Problems, and Sampling - Laura Petto
- New Techniques in Optimal Transport - James Ronan
**2020**- Pattern Avoidance in Inversion Sequences - Juan S. Auli
- The 2-Selmer Group of a Number Field - Ben Breen
- Synthetic Aperture Radar Image Formation with Uncertainty Quantification - Victor Churchill
- Applications of Probabilistic Combinatorics to Markov Chains, Redistricting, and Permuations - Chris Coscia
- Morita Equivalence of Graph and Ultragraph Leavitt Path Algebras - Michael Firrisa
- Evolutionary Kuramoto Dynamics - Elizabeth Tripp
**2019**- On the Arithmetic of Tiled Orders - Angelica Babei
- Orders in Quaternion and Central Simple Algebras - Sara Chari
- Combinatorial Proofs to Linear Algebraic Indenties - Melanie Dennis
- 2-group Belyi Maps - Michael Musty
- On Algebras of Low Rank and Belyi Maps - Samuel Schiavone
**2018**- Matched Products and Dynamical Models for Multiplex Networks - Daryl DeFord
- Intersections of Virtual Multistrings - David Freund
- Exploring Multiplexity with Evolutionary Game Theory and Complex Networks - Tommy Khoo
- Patterns in Time Series and Dynamical Systems - Katherine Moore
- Permutations: descents, cycles, and patterns - Justin Troyka
**2017**- c-Wilf equivalences of permutations - Tim Dwyer
- On-Line Algorithms and Reverse Mathematics - Seth Harris
- Linear Chord Diagrams with Long Chords - Everett Sullivan
**2016**- On the Poisson Relation for Lens Spaces - Dan Cianci
- Dynamics of Magnetic Flows on Nilmanifolds - Jonathan Epstein
- Orthogonal
Modular Forms - Jeffrey Hein

(An application to a Conjecture of Birch, Algorithms and Computations) - Uniform Avoidance Coupling, Design of Anonymity Systems and Matching Theory - Ewa Infeld
- Finite-type invariants of order one for framed and long virtual knots - Nicolas Petit
**2015**- Results on Minimizing Closed Geodesics - Ian Adelstein
- Equivalences on Patterns in Random Walks - Megan Martinez
- Multiplicative Problems in Combinatorial Number Theory - Nathan McNew
- A function-field analogue of Conway's topograph - Michael Wijaya
- Generalized Fourier Transforms and their Applicatons - Sarah Wolff
- Boundary integral methods and their applications - Lin Zhao
**2014**- Permutations Realized by Signed Shifts - Kassie Archer
- Pattern Avoiding Permutations and Rook Placements - Jonathan Bloom
- $C^*$-algebras associated to directed graphs - Danny W. Crytser
- The Arithmetic of Cyclic Subgroups - Zebediah E. Engberg
- $K$-Theory for Twisted Groupoid $C^*$-Algebras - Elizabeth A. Gillapsy
- Bijective Combinatorics of Reduced Decompositions - Zachary R. Hamaker
- Aligned Hierarchies for Sequential Data - Katherine M. Kinnaird
- Nuclearity and Exactness for Groupoid Crossed Product $C^*$-algebras - Scott M. Lalonde
- Refocussing and Virtual Legendarian Knots - Asa Levi
**2013**- Elliptic Curves from a statistical point of view - Avram Gottschlich
- Capture Time in Variants of Cops & Robbers Games - Natasha Komarov
**2012**- Algebras Counting Self-Intersections of Curves - Patricia Cahn
- Selectivity in central simple algebras and isospectrality - Ben Linowitz
- Products of distinct cyclotomic polynomials - Lola Thompson
**2011**- Firefighting on Geometric Graphs - Amir Barghi
- Coloring Posets and Reverse Mathematics - Jared Corduan
- Roto-Translation Space and the Visual Cortex - Gregory C. Petrics
- A Mallows Model for Coxeter Groups and Buildings - Paige E. Rinker
- The Bloch spectrum of a quantum graph - Ralf Rueckriemen
- Numerically explicit estimates for character sums - Enrique Treviño
**2010**- On the Importance of Phase in Improving Detection of Shared Genomic Segments - G. Genovese
- Refocusing of Null-Geodesics in Lorentz Manifolds - Paul Kinlaw
- On the Density of Abundant Numbers - Mitsuo Kobayashi
- A Metric for Homotopy Types - Nick Scoville
- Aperiodicity in Topological k-Graphs - Sarah Wright
**2009**- Proper Actions of Groupoids on $C^*$-algebras - J. Brown
- Groupoid Crossed Products - G. Goehle
- A Composition Formula for Asymptotic Morphisms - M. Mahoney
**2008**- Distinguishing Complete Sets with Respect to Strong Notions of Reducibility - B. Andersen
- Carmichael's Conjecture and the Unit Group Function - J. Bayless
- Results on Off-branch Numbers - J. Bourke
- A Sequence of Degree One Vassiliev Invariants for Virtual Knots - A. Henrich
- Fast Fourier Transforms for Inverse Semigroups - M. Malandro
- Prime Polynomials Over Finite Fields - P. Pollack