Michigan Math REU Projects
Summer 2012
Chaotic Planetary Dynamics in Post MainSequence 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 BerezinToeplitz 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
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 VallePoussin Kernel
Harsh Mehta
Advisor:
Hugh Montgomery
Forbenius Manifold of K3 LGmodel
Nonsymplectic Automorphisms of Prime Order on K3Surfaces
Rachel Suggs
Advisor: Yongbin Ruan
The Kreiss Stability Condition for Initial Boundary Value Problems
Michaela Wood
Advisor: Divakar Viswanath
2011
Summer 2011
Dispersive Quantization
Sudarshan Balakrishnan
Advisors: Professor Benson Muite
Numerical Integration of Black Hole Solutions to the Einstein/YangMills Equations
Rebekah Bartlett
Advisor: Professor Joel Smoller
A Multivariate Median in Banach Spaces and Applications to Robust PCA
David Bruce
Advisor: Professor Roman Vershynin
FPure 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 AgeStructure 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 R^{2 }
Daniel Smolkin
Advisor: Professor Ralf Spatzier
Convergence and Error Bounds of the TrotterKato
Scheme for the HJB equation in a twofactor model
Howard Xu
Advisor: Professor
Erhan Bayraktar
Summer 2010
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 ganglioncell 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 BeckerD¨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 BruhatTits 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 LFunctions Induced by a
Character Modulo a High Power of a Prime
Christopher Link
Advisor: Professor Djordje Milicevic
Heegaard Splittings and Bounds for Closed Hyperbolic 3Manifolds
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 3planes in 6space 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 TwoLayer 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 DescentLike Statistics for the Hyperoctahedral Group
Laurie Lai
Advisor: Kyle Peterson
Summer 2007
Subgame 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 HodgkinHuxley and FitzHughNagumo Models and Networks of O and Icells
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
ExPost 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 GridFree 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 LastPassage 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 BerezinToeplitz 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 TravelingWave Front Solutions in a Diffusive PredatorPrey 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 Rtree Results
Jeremy Cook
Advisor: Professor Elmas Irmak
On a conjecture concerning nonintersecting 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 ReceptorMediated Apoptosis: Fas Trimerization and FADD Recruitment
Ronald Lai
Advisor: Professor Trachette Jackson
The TemperlyLieb Functions on Totally NonNegative 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
Summer 2002
TemperleyLieb Algebra Research Project
Nina Palmo
Advisor: Professor Mark Skandera
Totally Nonnegative Matrices, Graphs, and the TemperleyLieb Algebra
Randolph Pistor
Advisor: Professor Mark Skandera
THE RELATION OF GRAPHS TO TOTALLY NONNEGATIVE MATRICES AND THE TEMPERLEYLIEB ALGEBRA
Michal Ostrowski
Advisor: Mark Skandera
Summer 2001
AN INVESTIGATION OF THE COUPLING OF GRAVITY TO AN SU(2)
YANGMILLS FIELD IN A DIRAC PARTICLE SYSTEM
Robert W. Easton
Advisor: Professor Joel Smoller
NONAUTOMATICITY:
A LOOK AT AUTOMATIC GROUPS
USING CAYLEY GRAPHS AND THE KBMAG PROGRAM
John Baker
Stacey Barbosa
Advisor: Professor Bryan Mosher
