Past Senior Honors Theses

The following is a list of recent senior honors theses and the faculty advisors. These theses are kept in a volume in the mathematics undergraduate office in 115 Vincent Hall. You are invited to view them if you are contemplating doing an honors thesis. Please note that due to the COVID-19 pandemic, viewing access to past theses is unavailable at this time.


Student Thesis Advisor
Nicholas Backes "Cohomology of Abelian Varieties with Certain Vector-Valued Coefficients" K-W.Lan
Bernardo Bianco Prado "An Overview of Invariant Manifolds and their Applications" P.Polacik
Noah Carpenter "The Hadamard Product and a Few Open Problems" A.Akhmedov
Emily Koithan "Projecting Combined Anthropogenic and Natural Ecosystem Dynamics to Restore the Planet While Feeding the World" R.McGehee
Sean Mcnally “Virtual Complete Intersections in Stanley-Reisner Rings and Smooth Fano Toric Varieties” C.Berkesch
Jacob Ogden “A Complexified Model of the Navier-Stokes Equations with FractionalvDissipation” V.Sverak
Rebecca Rechkin "Proving the Hook Length Formula" C.Berkesch
Calvin Roth "An Overview of Factoring Algorithms" D.Johnstone


Student Thesis Advisor
Manaswinee (Mansi) Bezbaruah “Numerical Simulations of Plasmons on Graphene" F.Santosa
Andrew Brettin “Ecological Management Practices Informed by Flow-kick Dynamics” R.McGehee
Jacob Elafandi “Use of Marching Algorithms to Detect Edges of Breakage on Scans of Bone Fragments” J.Calder
Logan Knorr “Ranking Systems in NCAA Men's Basketball” J.Rogness
Linda Peng “Fuzzy Logic and Its Applications to Insurance” R.Ashkenazi
Julie Sherman “Constraints on the Oceanic Carbon Sink Using Atmospheric Oxygen Data” R.McGehee
Warut Thawinrak "Bruhat Order and the Rook Monoid" V.Reiner


Student Thesis Advisor
Paul Aarsvold “Manifolds and the Shape of the Universe" J.Rogness
Bat-Orgil Batsaikhan “Generative Capsule Network” G.Lerman
Kelly Catlin “Finding an Optimal Velocity for a Race” Y.Mori
Maria Gilbert “Hurwitz Actions in Complex Reflection Groups” V.Reiner
Elena Hafner “Face Structure and Volume of the Birkhoff Polytope” G.Musiker
Owen Levin “Approximation Algorithms for Network Connectivity” V.Reiner
Ian McMeeking "Computing with Noncongruence Subgroups" B.Brubaker
Mark Richard “On Random Schrodinger Operators” W-K. Chen
Ryan Vogt “Detection of Non-Symmetric Balanced Configurations” R.Moeckel
Lucy Yang “Quadratic Operad Algebras Induce BV Algebras” A.Voronov


Student Thesis Advisor
Rejendra Beekie “Stability of Pinned Fronts in Nonlocal Equations" A.Scheel
Grant Goodman “The Poincare'-Hopf Theorem” A.Akhmedov
Tikhon Gritskevich “Factorization Homology and TQFT” A.Voronov
Morganne Igoe “A Comparison of Individual-Based and Mean Field Model Approaches as Applied to Vector-Borne Pathogen Spread” D.Nykamp
Grace Meyer “Modeling the Effects of Discount Rate Assumptions and Funding Levels on the Minnesota State Retirement System Defined Benefit Plans” R.Ashkenazi
Bradford Olson “Nim Take A All But B” B.Fristedt
Kobie Spaeth "Polling Errors and Their Effect on the Modeling of the 2016 Presidential Election" R.Ashkenazi
Samuel Stromwall “Effectiveness of Recursive Algorithms on Word Shortening” P.Webb
Han Yong Wunrow “Dynamics of Billiard Systems in Regular Polygons” R.Moeckel


Student Thesis Advisor
Benjamin Feigenbaum “One-Dimensional energy Balance Model" B.Maultsby
Christian Gaetz “Critical Groups and the McKay Correspondence” V.Reiner
Thomas Gebhart “Demand Drivers of Bitcoin” R.Ashkenazi
Joseph Lawson “Classification of Unlabeled Data” G.Lerman
Carolyn Reinhart “Moebius Functions and Euler Characteristics for Categories” P.Webb
Andrew Senger “The Spectral Artin Representability Theorem” T.Lawson
Marshall Smith "Cohomology of Braided Vector Spaces" C.Westerland
Kazmer Schmanski “A Probability Theory Framework for Baseball Strategy and Simulations” M.Weimerskirch
Di Wu “Is There a Set that Is Not Almost Open But Still Measurable in R?” S.Adams
Yao Rui Yeo “Dessin d'Enfants” V.Reiner


Student Thesis Advisor
Ethan Heinzen “Second-Order Neural Networks and Synchrony" D.Nykamp
Joel Knighton “The Immerman-Szelepcsenyi Theorem and the Second LBS Problem” W.Richter
Christopher Lovdal “The Critical Value of the Speed of an Interface Propagating Energy Relaxation” A.Scheel
Michael Neaton “Minimal Covers of Manifolds” T-J.Li
Anton Okhrimchuk “Monte Carlo and Quasi-Monte Carlo Methods of Integral Approximation” D.Bilyk
Yunpeng Shi “Experiments on Robust Camera Motion Estimation” G.Lerman
Maxwell Shinn "Synergy, Redundancy, and Integrated Information in the Brain" D.Nykamp
Benjamin Wilson “Infinite Hats: Cycle Structures of Large Permutations” G.Anderson
Fadumo Yusuf “Teaching Methods in Mathematics” M.Weimerskirch
Chelsea (Xi) Zhao “A Study on Capital Asset Pricing Model and Its Illustrations” R.Ashkenazi


Student Thesis Advisor
Benjamin Bachmeier "Modeling the Effects of Sea Ice on Phytoplankton Growth Dynamics" R.McGehee
Ana Liard-Blanco "Bernstein-Sato Polynomials" E.Witt
Haojun Caoxu "Reimann's 1859 Paper and the History of Complex Analysis" P.Garrett
Jason Checky "Branching Processes adn Cell Populations" J.Baxter
Andrew Dean "An Information Theoretic Study of Rhythmic Variations of Poetic Accents in Hip-Hop" D.Clark
Thomas Edwards "Discontinuous Galerkin Methods for Ordinary Differential Equations" B.Cockburn
Yifan Feng "Effect of Dynamic Pricing on Inventory Costs: A Mathematical Model" J.Baxter
Robin Heinonen "Contractions of Superintegrable Darboux Systems" W.Miller Jr.
Amber Hill "Linear Programming and Its Economic Applications" G.Anderson
John Karlen "Fermat's Principle and Its Applications" V.Sverak
Ryan Lee "Applications of Entropy Rates to Relative Poverty as a Measure of Longitudinal Economic Mobility" A.Scheel
Jiacheng Liao "A Study on Hidden Markov Model and Its Application" J.Baxter
Alexandra Nelson "Use of Color Exchange to Classify Regular Graphs of Order 12 by Power Sequence" J.Butterfield
Eric Seifert "An Expository of Elliptic Curve Cryptography" J.Butterfield
Haiyun Zhao "Matrix Nearness Problems with Indefinite Lorentz Metric" W.Miller Jr.


Student Thesis Advisor
Gong Chen "Vibrations of Suspended Chains" V.Sverak
Jean Costello "Proof of the AKS Primality Test" D.Stanton
Xavier Garcia "Pathological Billiards" R.Moeckel
Kelsey Gladen "Markov Chain Monte Carlo and Its Applications" J.Baxter
Matthew Howard "Chance Operations in Musical Compositions" L.Gray
John Kilgore "Exotic 4-Manifolds" A.Akhmedov
Matthew Larionov "Finite Model Theory and Logics for PTIME" W.Richter
Tyler Maunu "A Robust PCA Framework with Randomized Singular Value Decompositions" G.Lerman
Aaron Schneberger "Critical Groups of Certain Graphs and their Cryptographic Implementation" G.Musiker
Benjamin Tolzmann "Advanced Statistics and Prediction in American Professional Sports" A.Odlyzko
Thomas Vandenboom "Light-wave Localization Phenomena in Layered Dielectric Media" F.Santosa


Student Thesis Advisor
Wei Chen “On Certain Non-linear Second-order Ordinary Differential Equations and Applications" M-C Calderer
Patrick Floryance “Random Walks, Electrical Networks and Perfect Squared Squares” V.Reiner
Nathan Fox “Some Applications of the Mobius Function” P.Webb
Daniel Hess “Finiteness of the Stable Homotopy Groups of Spheres” T.Lawson
Xin Jin “Bandit Problems and Gitton-index Theorem” B.Fristedt
Madeleine Kotzagiannidis “The Triangular Distance Histogram in Object Recognition” P.Olver
Enming Mao "A Model of Order Book Dynamics" J.Baxter
David Nichols “Nonstandard Analysis As a Tool for Instruction and Discovery” W.Richter
Grant Remmen “Dynamics of a Rigid Spinning Ring in the Schwartzchild Metric: A Solution to a Gravitational Problem in Mathematical Physics” W.Miller
Jennie Schneider “The Fibonacci Number in Nature” A.Scheel


Student Thesis Advisor
Aaron Barkley "Projecting a Matrix onto the Special Linear Group" W.Miller
Bjorn Berntson "Analysis of Kepler-Type Problems in Non-Eudclidian Geometries of Constant Curvature using Superintegrability Methods" W.Miller
Matthew Coudron "A Note on Eigenvalues of Non-Hermitian Anderson Operators" G.Anderson
Christopher Fredregill "A Comparative Study of Markov Chain Monte Carlo Algorithms" C.Geyer, J.Baxter
Daniel Hoff "Differential Invariant Signatures for Object Recognition and Automatic Solutions of Jigsaw Puzzles" P.Olver
Eunjeong Jo "NTRU Encrypt Public Key Cryptosystem" A.Odlyzko
Li Lin "Compressive Sampling" W.Miller
Cordelia McGehee "Parasites and Peristalsis: Towards a Computational Understanding of A.suum Motility in the Small Intestine" H.Weinberger
Chatanya Rachabattuni "Flow of Particles in Dynamical Model Systems" W.Miller
Sean Vig "Periodic Orbits of the Isosceles Three Body Problem and Their Stability" R.Moeckel


Student Thesis Advisor
Danielle Sandler "The Implications of 2nd Orter Motifs on Neural Network Structure" D.Nykamp
Max Siegel "Large Deviations and Statistics" O.Zeitouni


Student Thesis Advisor
Dan Brinkman "Invariant Histograms" P.Olver
Joseph Loubert "Bott Periodicity" T.Lawson
Tom Vacek "Ehrhart Reciprocity" S.Sperber


Student Thesis Advisor
David Barta “An Introduction to Gaussian white noise analysis in sensory system Neurophysiology” D.Nykamp
John Bergdall “Aspects of the Theory of p-Adic Galois Representations” W.Messing
Derek Dalle “Invariant Numerical Approximations to EquiAffine Curvature using Moving Frames” P.Olver
Andrew Hampton “A Finite Expression of FO-Inexpressibility” W.Richter
Robert Hank “Using Spectral Sequences to Compute Homology” T.Lawson
David Morrissey “Mathematical Modeling of Point Vortices” M-C Calderer, D.Spirn
Nicholas Switala “p-Divisibility of the number of F_p rational points on certain hypersurfaces” S.Sperber
Rebecca Weiler “An Introduction to Minimizing Energy Functions” M-C Calderer


Student Thesis Advisor
Dan Colestock “Growth Distributions and Enumerations of Subtrees” B.Fristedt
Bradley Froehle “An Introduction to Combinatorial Garside Structures” P.Webb
Alexander Miller “Smith Invariants and Dual Graded Graphs” V.Reiner