PAST VIGRE REU PROJECTS 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 Summer 2002 Temperley-Lieb Algebra Research Project Nina Palmo Advisor: Professor Mark Skandera Totally Nonnegative Matrices, Graphs, and the Temperley-Lieb Algebra Randolph Pistor Advisor: Professor Mark Skandera THE RELATION OF GRAPHS TO TOTALLY NONNEGATIVE MATRICES AND THE TEMPERLEY-LIEB ALGEBRA Michal Ostrowski Advisor: Mark Skandera Summer 2001 AN INVESTIGATION OF THE COUPLING OF GRAVITY TO AN SU(2) YANG-MILLS FIELD IN A DIRAC PARTICLE SYSTEM Robert W. Easton Advisor: Professor Joel Smoller NON-AUTOMATICITY: A LOOK AT AUTOMATIC GROUPS USING CAYLEY GRAPHS AND THE KBMAG PROGRAM John Baker Stacey Barbosa Advisor: Professor Bryan Mosher