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