Here is a list of all of the student research projects I have supervised. The list includes some from previous job (which are labeled), so goes back to 2003-2004.
Undergraduate Reading Projects
- the (2,3,7)-tiling of the hyperbolic disk,
- geometric ordinary differential equations,
- peg-board games,
- Clifford-Klein space form problem (Williams College),
- Fuchsian groups (Rice U.),
- representations of Lie algebras in physics (Rice U.)
Undergraduate Research Projects
- fundamental domains for Hilbert modular groups (an Honors Thesis), Alyssa Soenksen 2007-2008
- m-ary partitions (two projects),
- symmetry of structure polynomials for m-ary partition functions, Mackenzie Roepke, 2008-2010
- divisibility of m-nomial coefficients, Duncan Wright, Summer 2011-Spring 2012
- ambigrams (an Honors Thesis, second adviser), Callie Kronlage, 2008-2009
- large metric spaces with non-positive curvature (three separate projects on this topic)
- The isometry group of a Continuum Product, Corey Gevaert, Summer 2009
- Algebraic characterization of the isometries of a continuum product, Kyle Pitzen & Joe Winder, 2009-2010
- Metric non-decreasing coordinates on a countable product of hyperbolic planes, Kyle Pitzen, 2010-2011
- curve shortening for polygons (two projects)
- Menger Curvature Transformation for Polygons, Jesse Moeller, 2012-2013
- CURM funded project on Polygon Shortening Flows, Jesse Moeller, Jon Krein, Abby Parker & Ben Castle, 2013-2014
- Knot theory
- Bridge Indices for some 12-crossing prime knots, Julie Kirkpatrick & Tracey Wulfekuhle, Spring 2016
- Algorithms for Bridge Index Hand Computation, Julie Kirkpatrick, Fall 2017
Master’s Reading Projects
- Harmonic Functions on Cayley graphs and Gromov’s theorem on polynomial growth Mary Gilles, 2010-2011
- Plotting Limit Sets of Linear Fractional Transformations Using Sage Corey Gevaert, Spring 2012
- second reader for several Master’s in Mathematics Education (Secondary) papers
Master’s Thesis Projects
- Einstein Metrics on Piecewise-Linear 3-spheres Kyle Pitzen, Summer 2013
- A Survey of Butterfly Numbers for Knots and Links, Mark Ronnenberg, Spring 2017
- A Naïve Computational Approach to the Bridge index of a knot, Genevieve Johnson, expected Fall 2017