PAST VIGRE REU PROJECTS 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