# History of REU and SPUR (Summer Program for Undergraduate Research) Programs

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# Undergraduate Research Programs

The Mathematics Department has offered a summer research program for undergraduates for many years. Prior to 2015 the REU Program (Research Experiences for Undergraduates) funded by the NSF (National Science Foundation) was offered. From 2015 - 2017 after the grant temporarily expired, the program transitioned to a non-funded program named SPUR (Summer Program for Undergraduate Research), which offers the same opportunity to undergraduate students, but the only difference in the two programs is funding. Beginning in 2018 the REU Program returned, and the department has continued both programs. These are 8-week programs that provide an opportunity for undergraduate students of mathematics to participate in leading-edge research. Projects are offered every summer, each led by an expert in the field.

Previous Years' Projects and Some Results

#### 2021 - REU and SPUR

- Loop groups and Verlinde algebra - SPUR
- Theoretical aspects of deep learning - REU

#### 2020 - REU and SPUR

- Mechanics and Manipulation of Active Structures, directed by Andy Borum - SPUR
- Analysis and Implementation of Spectral Methods, directed by Alex Townsend - REU

#### 2019 - REU and SPUR

- Analysis on Fractals, directed by Robert Strichartz - SPUR
- Computations in Derived Algebraic Geometry and Equivariant Cohomology, directed by Harrison Chen - SPUR
- Mechanics, Control, Robotics, and Dynamics, directed by Andy Borum - REU

#### 2018 - REU and SPUR

- Analysis on Fractals, directed by Robert Strichartz - SPUR
- Topological Methods in Discrete Geometry, directed by Florian Frick - SPUR
- Generating Sets of Finite Groups, directed by Keith Dennis - SPUR
- Optimality and Uncertainty, directed by Alex Vladimirsky - REU

#### 2017 - SPUR

- Analysis on Fractals, directed by Robert Strichartz
- Topological Methods in Discrete Geometry, directed by Florian Frick
- Generating Sets of Finite Groups, directed by Keith Dennis

#### 2016 - SPUR

- 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 - SPUR

- 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
- 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
- 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
- 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

- Analysis on Fractals (Robert Strichartz)
- Games, Linear Orders, and Logic (Francois Dorais)
- Topological Dynamics, Group Actions, and Cantor Set n-Cubes (Collin Bleak)

#### 2007

#### 2006

#### 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