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 2020 COVID-19 pandemic, viewing access to past theses is unavailable at this time.
2019-2020
| 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 |
2018-2019
| 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 |
2017-2018
| 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 |
2016-2017
| 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 |
2015-2016
| 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 |
2014-2015
| 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 |
2013-2014
| 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. |
2012-2013
| 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 |
2011-2012
| 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 |
2010-2011
| 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 |
2009-2010
| 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 |
2008-2009
| Student | Thesis | Advisor |
|---|---|---|
| Dan Brinkman | "Invariant Histograms" | P.Olver |
| Joseph Loubert | "Bott Periodicity" | T.Lawson |
| Tom Vacek | "Ehrhart Reciprocity" | S.Sperber |
2007-2008
| 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 |
2006-2007
| 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 |