Summer 2014

Tropical Constructions and Lifts
Author: Hunter Ash
Advised by: Prof. Tyler Foster

Modeling Type One Diabetes with a Linear Response Function Based Model
Authors: Matthew Bauerle and Xinyan Han
Advised by: Prof. Yaniv Plan and Prof. Roman Vershynin

Biases in statistical inference: measles as a case study
Author: Alexander Becker
Advisor: Prof. Aaron King

Invariant Distributions on l-spaces
Author: Ben Brady
Advisor: Prof. Stephen DeBacker

A Permutation Model with Finite Partitions of the Set of Atoms as Supports
Author: Benjamin Bruce
Advisor: Prof. Andreas Blass


Substitution Polynomials and the Decomposition of Rational Functions

Author: Eric Levin
Advisor: Prof. Danny Neftin

Relatively Prime and Squarefree Integers
Author: Nora Farouk
Advisor: Prof. Patrick Boland

Exploring the Geometric Model of Riffle Shuffling
Authors: Jieun Lee, Janine Lewandoski, and Kevin Reifor
Advisor: Prof. Mark Conger

Elliptic Curves and Their Torsion
Author: Siyan “Daniel” Li
Advisor: Prof. Ian Shipman


Effect of Transaction Tax on Optimal Portfolio Liquidation and Predatory Trading

Author: Enkhjargal Lkhagvajav
Advisor: Prof. Sergey Nadtochiy

On Robust Arm-Acquiring Bandit Problems
Author: Shiqing Yu
Advisor: Prof. Xiang Yu

Sleep-wake cycles and jet lag
Author: Channa Schramm
Advisor: Prof. Victoria Booth

Hyperbolic geometry and moonshine groups
Author: Bazyli Szymanski
Advisor: Prof. Pat Boland


The Number of Generators of the First Koszul Homology of an Artianian Ring

Author: Alex Zhongyi Zhang
Advisor: Prof. Mel Hochster

Fund Manager's Portfolio Choice
Author: Zhiqing Zhang
Advisor: Prof. Gu Wang


Summer 2013

Monte Carlo Valuation of High Dimensional American Options
Author: Michael Angileri
Advised by: Dr. Arash Fahim

A Fast Algorithm to the RadiativeTransport Equation and Implementation of 
Theory Into an Applet
Author: Mihai V. Avram
Advised by: Manabu Machida

Monomial Valuations, Cusp Singularities, and Continued Fractions
Author: David Bruce and Molly Logue

Extended Vamos Matroids and the Half-Plane Property
Author: Sam Burton and Yewon Youm

Numerical Methods for the One Way Water Wave Equation
Author: Sean Carney
Advised by: Smadar Karni

Data Assimilation using Optimal Control and Kalman Filtering
Author: Wei Chen and Evelyn Lunasin

Investigating Hyperbolic Geometry
Author: Sean Douglas and Caleb Springer

An Alternative Model for Card Shuffling
Author: Christopher Drouillard

Central Simple Sugeralgebras and the Spin Group
Author: Benjamin Gammage

Binary Matrix Completion and its Application to Restaurant Recommendation System
Author: Chenrui Gao
Advisors: Prof. Yaniv Plan, Prof. Roman Vershynin

Fundamental Domain and Hyperbolic Geometry
Author: Yubo Guo

Staircase ribbons in Sn
Author: Colin Holmes

Seeking Mechanisms Behind the Formation of Synchronized Behavior in 
Cellularly Diverse Neural Networks
Author: Scott Knudstrup
Advisors: Victoria Booth

Multicategory and Monoidal Category
Author: Luhang Lai

Weakly Circle-Preserving Maps in Inversive Geometry
Author: Joel C. Gibbons and Yusheng Luo

Optimizing Snake Locomotion
Author: Matthew Osborne
Advisor: Professor Silas Alben

Time Series of Implied Density
Author: Wonho Rhee
Advisor: Prof. Sergey Nadtochiy

Polynomial Identities on Eigenforms
Author: Joseph Richey and Noah Shutty

Mathematical Model and Analysis of Cellular Diffusion
Author: Dylan Corey Sena

Modeling Retinal Neurons
Author: Jonathan Timkovich

A Bound on Length Isospectral Families and Applications
Author: Weston Ungemach

Discrete Groups of Isometries and Fundamental Domains
Author: Yutong Wang
Advisor: Patrick Boland, Lizhen Ji

On Multivariate Path-Dependent Pricing 
Author: Zhiyuan Wang
Advisor: Xiang Yu

Computations in the Lie Algebra of F4 and a Parameterization of Nilpotent Orbits
Author: Karl Winsor
Advisor: Stephen DeBacker

 

Summer 2012

Chaotic Planetary Dynamics in Post Main-Sequence Stellar Systems
Kassandra Anderson
Advisors: Fred Adams & Anthony Bloch

Random Matrices with Prescribed Row and Column Sums
Dangxing Chen
Advisor: Alexander Barvinok

Towards a Szego Limit Theorem for Berezin-Toeplitz Operators with Singular Symbols
Tyler Friedman
Advisor: Alejandro Uribe

Calculations on a Lattice L Spanned by a Set of Conformal Vectors
Todd Gaugler
Advisor: Robert Griess

Commutators in the Metaplectic Group
Daniel Hast
Advisor: Dmitriy Boyarchenko

Non-consecutive Congruences of Dedekind-finite Sets
Author: John Holler and Matthew Tanzer
Advised by: Andreas Blass

Examining the Sample Complexity of the Maximum Likelihood Estimator in
Phylogenetic Tree Reconstruction
Sangwon Hyun
Advisor: Jose Alcala Burgos

Fundamental Domains of Discrete Groups Acting on Euclidean Space
John Kilgore
Advisor: Lizhen Ji

Quiver Representations
Molly Logue
Advisor: Harm Derksen

L1 Norm of the Valle-Poussin Kernel
Harsh Mehta
Advisor: Hugh Montgomery

Forbenius Manifold of K3 LG-model
Non-symplectic Automorphisms of Prime Order on K3-Surfaces
Rachel Suggs
Advisor: Yongbin Ruan

The Kreiss Stability Condition for Initial Boundary Value Problems
Michaela Wood
Advisor: Divakar Viswanath


Summer 2011

Dispersive Quantization
Sudarshan Balakrishnan
Advisors: Professor Benson Muite

Numerical Integration of Black Hole Solutions to the Einstein/Yang-Mills Equations
Rebekah Bartlett
Advisor: Professor Joel Smoller

A Multivariate Median in Banach Spaces and Applications to Robust PCA
David Bruce
Advisor: Professor Roman Vershynin

F-Pure Thresholds
Sifat Rahman & Joseph Billian
Advisor: Professor Bhargav Bhatt

Explorations in Genetic Oscillators
Christopher Chung
Advisor: Professor Richard Yamada

Face Vectors of Sphere Products
Kit Clement
Advisor: Patrick Boland

Modeling Human Sleep Patterns
Rebecca Gleit
Advisor: Professor Victoria Booth

Analysis of Mutual Predation in an Age-Structure System
Nathan Golovich
Advisor: Professor Charles Doering

Exploring KGH Bounds in t = 4
John Holler and Nick Wasylyshyn
Advisor: Professor Brett Hemenway

Zeta Functions, the Tate Conjecture, and Catanese Surfaces
Paul Lewis
Advisor: Professor Christopher Lyons

The Evolution of One Dimensional Crystal Surfaces in Two Configurations
Mark Liu
Advisor: Professor Hala Al Hajj Shehadeh

Calculation Process for a Star with Magnetic Field
Xiaotong Suo McClure
Advisor: Professor Joel Smoller

An Analysis of Position Probability Distributions of Trilateration
and Triangulation for Extremely Deep Space Navigation
David McMillon
Advisor: Professor Mark Conger

Geodesics of Periodic Metrics on R2
Daniel Smolkin
Advisor: Professor Ralf Spatzier

Convergence and Error Bounds of the Trotter-Kato
Scheme for the HJB equation in a two-factor model
Howard Xu
Advisor: Professor Erhan Bayraktar0

Establishing Conditions for REM Cycling in Different Networks
Aparna Ananthasubramaniam
Advisors: Professors Cecilia Diniz Behn and Victoria Booth

A quantitative study of the triangulated molecular surfaces perturbations caused by small displacements of the atomic centers
Mo Bai
Advisor: Professor Weihua Geng

Dark Halo Orbits and Tidal Stripping With the Spirographic Approximation
Rebekah Bartlett
Advisor: Professor Anthony Bloch

Tumor Angiogenesis
James Brunner
Advisor: Professor Trachette Jackson

Mathematically modeling the light responses of ganglion-cell photoreceptors
Samuel Faught
Advisor: Professor Daniel Forger

Investigations of Coupled Oscillators
Kara Fulton
Advisor: Professor Richard Yamada

Computation of Equilibrium Measures and Other Quantities of Interest for Random Matricies
Asad Lodhia
Advisor: Professor Jinho Baik

Pattern Avoidence on Arch Connected Graphs
Benjamin Kornacki
Advisor: Professor Pavlo Pylyavskyy

Sums of Isometric Pairs of Lattices
Paul Lewis
Advisor: Professor Robert Griess

Impulse Control of MultiDimensional Jump Diffusions with Infinite Variation
Christopher Link
Advisor: Professor Erhan Bayraktar

Checking For Isomorphism in Circulant Graphs
Augustus Odena
Advisor: Professor Michael Zieve

REU Paper 2010
Claudia Raithel
Advisor: Professor Anthony Bloch

Characterization of the full degree 2 del Pezzo Surface over the field of nine elements
Daniel Smolkin and Erin Kelly
Advisor: Professor Amanda Knecht

On the 2D Orientation Preserving Crystallographic Groups
Kyle Sinclair and Pearce Washabaugh
Advisor: Professors Christopher Mooney and Ralf Spatzier

An Algebraic Approach to Conformal Eld Theory
Yang Xiu
Advisor: Professor Igor Kriz


Summer 2009

Affine Alternating Sign Matrices
Michael Bennett
Advisor: Professor Pavlo Pylyavskyy

A Universal Degree Bound for Rings of Invariants of n Point Configurations Modulo Torus Actions
Jonathan Brito
Advisor: Professor Benjamin Howard

A Mathematical Model of Tumor Growth and Angiogenesis
Akshay Desai
Advisor: Professor Trace Jackson

A Model of Suprachiasmatic Nucleus Firing Rate in the Rodent
Michelle Fleshner
Advisor: Cecilia Diniz Behn

Long Time Behavior of a Modified Becker-D¨oring System: Initial Conditions Without Compact Support
Lee Gunderson
Advisor: Professor Peter Smereka

Singularities of Logarithmic Potentials at Analytic Corners
Boaz Haberman
Advisor: Professor Divakar Viswanath

Algorithms for Threat Detection: An Inverse Boundary Value Problem
Casandra Hall
Advisor: Professor Selim Esedoglu

Analyzing Tori in Split Groups over Quasifinite Fields via Bruhat-Tits theory
Wade Hindes
Advisor: Professor Stephen DeBacker

Developing Stochastic and Deterministic Models of Quorum Sensing
Tyler Johnson
Advisor: Richard Yamada

The Recursive Computatibility of Hyperelliptic Hodge Integrals with at Least One 1 Class
Andrew Kiluk
Advisor: Professor Renzo Cavalieri

The Effects of Varying Connectivity Strength on the Frequency of Inhibitory Neurons in Several Network Types
Khalid Kunji
Advisor: Professor Victoria Booth

Reconstruction and prediction of chaotic signals
Xuan Liang
Advisor: Professor Divakar Viswanath

Improving the Upper Bound on Dirichilet L-Functions Induced by a
Character Modulo a High Power of a Prime
Christopher Link
Advisor: Professor Djordje Milicevic

Heegaard Splittings and Bounds for Closed Hyperbolic 3-Manifolds
Brian Mann
Advisors: Professors Richard Canary and William Breslin

Linear Factors and the Pollard Rho Method
Brian Nixon
Advisor: Professor Harm Derksen

The 100% Off Auction:
Daniel Russo
Advisor: Professor Tilman Borgers

Using periodic orbits to predict trajectories on the Lorenz attractor
Kirill Serkh
Advisor: Professor Divakar Viswanath

Approximating Dendrimer Bonding Site Locations
Stephen VandenBrink
Advisor: Professor Jack Waddell

The Thermodynamics of Solid Tumor Growth: A Continuum Mechanics Approach
Sarah Verner
Advisor: Professor Krishna Garikipati

The Caldero degenerations of the Grassmannian of 3-planes in 6-space and the positive tropical G(3,6)
Seth Wolbert
Advisor: Professor Benjamin Howard


Summer 2008

The Kernel of a Derivation on the Field of Rational Functions and the Zariski Closure of Local Integral Curves
Wade Hindes
Advisor: Professor Harm Derksen

Mathematical Models for Quorum Sensing in Vibrio harveyi and Pseudomonas aeruginosa
Kaytlin Brinker
Advisor: Professor Jack Waddell

Model of an Orexin Neuron
Katie Williams
Advisor: Cecilia Diniz Behn

Tropical Intersections and Shadow Points
Alex Larson
Advisor: Renzo Cavilieri

Coexistence of Multiple Parasitoids on a Common Host in a Globally Connected Metapopulation
Benjamin Berman
Advisor: Aaron King

Total Promotion
Kevin Dilks
Advisor: Kyle Peterson

Properties of Steady State Solutions for Critical Two-Layer Shallow Water Flows
Alfredo Wetzel
Advisor: Smadar Karni

Synchronization of Signaling Systems
Hasan Cheema
Advisor: Daniel Forger

An Equivalent Condition for the Reducibility of Tropical Curves
Brian Mann
Advisors: Hannah Markwig and Renzo Cavalieri

Generalising Cut and Join and Recursions of Hurwitz Numbers
Andrew Kiluk
Advisor: Renzo Cavalieri

Equidistribution of Descent-Like Statistics for the Hyperoctahedral Group
Laurie Lai
Advisor: Kyle Peterson


Summer 2007

Sub-game Perfect Equilibria of the Simultaneous Ascending Auction
Brian Baisa
Advisor: Professor Tilman Börgers

Steinberg Complexes and Affine Descents
Kevin Dilks
Advisor: Professors Kyle Petersen and John Stembridge

Action Potential Behavior in Hodgkin-Huxley and FitzHugh-Nagumo Models and Networks of O and I-cells
Stephen Gao
Advisor: Professor Victoria Booth

Optimization of Hydroelectric Pumped Storage: An Extension of Optimal Switching
Anthony Kuehne
Advisor: Professor Michael Ludkovski

Level Sets of the Takagi Function and Hausdorff Dimension
Zachary Maddock
Advisor: Professor Jeffrey Lagarias

Working with Maple
Anna M. Musial, Sam L. Rosenbaum
Advisor: Professor Arthur Wasserman

Two New Exceptional Quivers of Finite Mutation Type
Theodore Owen
Advisor: Professor Harm Derksen

Hyperelliptic Hodge Integrals
Peter Troyan
Advisor: Professor Renzo Cavalieri

Changes in Betti numbers of Hessenberg varieties on restricted tableaux
Derek Van Farowe
Advisor: Professor Julianna Tymoczko

Properties of Steady State Solutions for Shallow Water Flows
Alfredo Wetzel
Advisor: Professors Smadar Karni and Jorge Balbas

Ternary Basic Digit Sets
Christopher J. Young
Advisor: Professor Jeffrey Lagarias


Summer 2006

Ex-Post Equilibria in Games of Incomplete Information
Timothy McQuade
Advisor: Professor Tilman Borgers

The Gap Size Distribution of Parked Cars and the Coulomb Gas Model
Anthony Fader
Advisor: Professor Jinho Baik

Properties of the Takagi Function
Zachary Maddock
Advisor: Professor Jeffrey Lagarias

Virtual Cathode Simulation in 1D using a Grid-Free Poisson Solver
Ying Ki Yim
Advisor: Professor Lyudmyla Barannyk

Probabilistic Interpretations of Variables in Transient M/G/1 Random Walks
Drew Bollinger and David Wheeler
Advisor: Professor B.A. Taylor


Summer 2005

A Generalization of Conway Number Games to Multiple Players
Christopher Cunningham
Advisor: Professor Igor Kriz

Efficient And Accurate Unstructured Mesh Generation
Matthew Elsey
Advisor: Professor James Rossmanith

A Transformation Of A Standard Random Walk
Jason Goldstick
Advisor: Professor Joseph Conlon

Using Lattice Packings to Create Extended Codebooks
Daniel Sikora
Advisor: Professor Anna Gilbert

Directed Last-Passage Site Percolation with Bernoulli Site Distribution
Robert Hines
Advisor: Professor Jinho Baik

Dynamics of Interacting Point Charges and Vortices within a Constant Magnetic Field
Stephen Marin
Advisor: Professor Andrew Christlieb and Robert Krasny


Summer 2004

Momentum Matching for the Pendulum on Cart Problem
Esha Krishnaswamy
Advisor: Professor David Schneider

Linear Perturbations of a Class of Berezin-Toeplitz Operators
Adam Bendorf
Advisor: Professor Alejandro Uribe

New Results in Extremal Number Theory
Randolph Pistor
Advisor: Professor Kannan Soundararajan

Homeomorphism Groups of the Sierpinski Carpet and Sierpinski Gasket
Joel Louwsma
Advisor: Professor Bruce Kleiner

Computing Traveling-Wave Front Solutions in a Diffusive Predator-Prey Model
Brian Kim
Advisor: Professor Gregory Lyng

Inversions Within Restricted Fillings of Young Tableaux
Sarah Iveson
Advisor: Professor Julianna Tymoczko

Stabilization of Inverted Pendulum Systems
David Aristoff
Advisor: Professor Tony Bloch

An Overview of Green's Functions on Metrized Graphs
Douglas Li
Advisor: Professor Mattias Jonsson

Some R-tree Results
Jeremy Cook
Advisor: Professor Elmas Irmak

On a conjecture concerning non-intersecting congruence classes
Robert Hines
Advisor: Professor Kannan Soundararajan

The Problem of Type
Charles Crissman
Advisor: Professor Mario Bonk

The Likelihood of Cyclic Results in Pairwise Elections
Greg Malivuk
Advisor: Professor Divakar Viswanath


Summer 2003

Inverted Double Planar Pendulum on a Cart: Feedback Stabilization Using the Method of Controlled Lagrangians
David G. Aristoff
Advisor: Professor Anthony Bloch

A Mathematical Model of Receptor-Mediated Apoptosis: Fas Trimerization and FADD Recruitment
Ronald Lai
Advisor: Professor Trachette Jackson

The Temperly-Lieb Functions on Totally Non-Negative Matrices
Brendon Rhoades
Advisor: Professor Mark Skandera

Schur Positivity Conjectures about Temperly Lieb functions on Jacobi Trudi Matrices
Sean Gerrish
Advisor: Professor Mark Skandera

Dynamical Systems and Circle Maps
Ronit Slyper
Advisor: Professor Nikola Petrov

RELATIONS IN N[X] LEADING TO FINITE DIMENSIONAL POLYNOMIAL RIGS AND
EPIMORPHIC IMAGES OF N
Bertrand J. Guillou
Advisor: Professor Andreas Blass