Previous Undergraduate Summer Research Projects

2016

• Analysis on Fractals, directed by Robert Strichartz

• Topological Methods in Discrete Geometry, directed by Florian Frick

  • On Reay's relaxed Tverberg conjecture and generalizations of Conway's thrackle conjecture

• Nonlinear Heat Equations, directed by Xiaodong Cao

2015

• Analysis on Fractals, directed by Robert Strichartz

• Harmonic Analysis on Stiefel Manifolds, directed by Raul Gomez

• Graphs, Chip-Firing Games, and Algebraic Geometry, directed by Farbod Shokrieh

2014

• Analysis on Fractals, directed by Robert Strichartz

  • The Abelian Sandpile Model on Fractal Graphs

  • Surfaces with Fractal Curvature

• Nonlinear Heat Equations, directed by Xiaodong Cao

• Graphs, Chip-Firing Games, and Algebraic Geometry, directed by Farbod Shokrieh

2013

• Analysis on Fractals, directed by Robert Strichartz

  • Peano Curves and Laplacians on Fractals

  • Quantum Mechanics on Fractals

• Generating Sets for Finite Groups, directed by Keith Dennis

• High Dimensional Data Analysis, directed by Matthew Hirn

2012

• Analysis on Fractals, directed by Robert Strichartz

  • K-Forms on Carpet Type Fractals

• Packings and Tilings, directed by Robert Connelly

• The Heat Equation, directed by Xiaodong Cao

2011

• Analysis on Fractals, directed by Robert Strichartz

• Generating Sets for Finite Groups, directed by Keith Dennis

• Combinatorics of Triangulations, directed by Ed Swartz

2010

• Analysis on Fractals, directed by Robert Strichartz

• Geometric Differential Equations, directed by Xiaodong Cao

• Optimality and Uncertainty, directed by Alexander Vladimirsky

2009

• Analysis on Fractals (Robert Strichartz)

• Solving Games on Graphs, Fast (Sasha Rubin)

• Groups via Actions (Collin Bleak)

2008

• Laplacians on Julia Sets

2007

• Outer Approximation of the Laplacians of Random Carpets and Julia Sets

2006

• Self-Similar Laplacian on the Sierpinksi Gasket with Twists

• Higher Dimensional Sierpinski Gaskets

Older Work

• Conformal Energy, Conformal Laplacian, and Energy Measures on the Sierpinski Gasket

• Approximating the Laplacian on Fractal Domains as a Limit of the Plane Laplacian on Domains Approaching the Fractal

• Geometry of Numbers Work 2001

• Karl Papadantonakis Henon Mapping Work (and some other)

• Medusa Program for Polynomial Matings

• Finite Elements on the Sierpinski Gasket

• Differential Equations on the Sierpinski Gasket

• Harmonic Mappings of the Sierpinski Gasket

• Sampling Theory for Functions with Fractal Spectrum

• Sampling on the Sierpinski Gasket

• Fourier Series on the Sierpinski Gasket

• P-Energy on the Sierpinski Gasket (2001)

• P-Energy on Sierpinski Gaskets (2002)

• Pentagasket Research (Alex Smith)

• Polynomials and Power Series on Sierpinski Gaskets

• Levy's Dragon

• FEM on Sierpinski Gaskets

• Periodic Solutions to Forced Van der Pol

• Forced VdP, Bifurcation Diagram, Canards

• FVDP Summaries and Auto Work

• Surfaces Related to Henon Maps and the Program Cubism

• Work from 1998