Undergraduate Research Programs

The Mathematics Department has offered a summer research program for undergraduates for many years. Formerly an REU and now called SPUR, the 8-week program provides an opportunity for undergraduate students of mathematics to participate in leading-edge research. We offer three projects every summer, each led by an expert in the field.

See the SPUR 2017 program announcement for information about this year's program, including project descriptions and application instructions.

Previous Years' Projects and Some Results

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