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Undergraduate Research

Summary

This page contains details about research projects, honors theses, and special studies that I have advised. You can also find information about mentoring, as well as some talks for undergraduates and high school students that I have given.

Interested in Graduate school in the mathematical sciences? Click here for information.

Research Experiences for Undergraduates

A folded (5,2) torus knot from the Knot Atlas.

At Washington & Lee University

  • Summer 2020 John Carr Haden (’22) and Troy Larsen (’22) worked on the folded ribbon knot project. Their results are in their report Minimizing Ribbonlength for Folded Ribbon Knots found here.
  • Summer 2018 Corinne Joireman (’21) and Allison Young (’20) worked on Knot theory and tie knots. Click here for a talk about their results given at UnKnot IV at UW Bothell July 19-21, 2019.
  • Summer 2015 Emily Jaekle (’16) and Ryan McDonnell (’17) worked on Mathematics and 3D printing. Click here for their results.
  • Summer 2014 Mary Kamp (’15) and Xichen (Catherine) Zhu (’17) continued work on the Folded ribbon project. Their results are found here in the paper Ribbonlength of folded ribbon unknots in the plane.

Elsewhere:

  • Fall 2011 Smith College: Eleanor Conley, Emily Meehan, Rebecca Terry worked on Folded ribbon knots in the plane. They presented their results at Jan 2012 Joint Math Meetings, Boston, MA. Click here for their report (8.3 MB).
  • Summer 2009 Smith College: Shivani Aryal, Shorena Kalandarishvili and Sarah Meyer studied flat knotted ribbons. These are knots and links constructed from a rectangle of fixed width which is then folded flat in the plane. They presented their research at the Unknot Conference 2009 at Dennison University, OH. Click here for their report (2.4 MB).
  • Summer 2007 Smith College: Reagin (Taylor) McNeill studied the supercrossing number of knots.
  • Summer 2005 Harvard University: Gerardo Con Diaz’s project included a study of the supercrossing number of knots.
    Click here for his report (3.1 MB).
  • Summer 2004 Harvard University: Gerardo Con Diaz’s project included an introduction to knot theory, seifert surfaces, signature of a knot and proving that (2,2n+1) torus knots have signature 2n for any integer n. Harvard University.
  • Summer 2001, 2002 University of Illinois, Urbana-Champaign: Associate mentor for NSF funded illiMath2001 and illiMath2002 REUs in geometry in the Mathematics Department. The project developed a java applet visualizing the crossing map. This software was developed further at Technische Universitat Berlin into a project titled “Visualization in geometric knot theory”, and can be found here.

Honors Theses

At Smith College

  • Emma Schlatter (’10) Knot theory and its application to 3-manifolds. Click here for her thesis (1 MB).
  • Reagin (Taylor) McNeil (’08) Knot Theory and the Alexander Polynomial. Click here for her thesis (1.2 MB). In 2013 Taylor graduated with a PhD in mathematics from Rice University.

Special Studies

At Smith College

  • Spring 2011 Viktoria Pardey: Algebraic Topology
  • Fall 2009 Emma Schlatter (’10), Nicole Vitale (’10): Introduction to algebraic topology.
  • Spring 2008 Rosanna Speller (’08): The minimum distance energy of knots. A poster (284KB) of her work was shown at Smith Collaborations ’08. Click here for her report (204 KB)

Mentoring

Interested in graduate school in mathematics? Please stop by for a chat and we can discuss what’s involved. It’s usually best to start early and work on your applications bit by bit each week. Click here for more information.

In Fall 2012, 2013, 2014, 2016 and 2017 I organized a mathematics GRE prep session jointly with another faculty member at WLU.

I was the organizer of a panel on Life as a graduate student at the 2009 Women In Mathematics In New England Conference held at Smith College on Saturday September 26, 2009. We discussed how to find a graduate school and apply, and give tips on being a successful math graduate student. (This is a repeat of the very successful discussion I moderated at WIMIN ’08.)

I mentored a number of students from the Center for Women in Mathematics at Smith College. They have since gone on to graduate school in mathematics and some are now graduating with PhDs in mathematics.

I was a mentor for Gerardo Con Diaz, a Mellon Mays Undergraduate Fellow in mathematics at Harvard University. He has since graduated with a PhD in the philosophy of science from Yale University.

Introductory Talks

Spring 2022 Rectangles, squares, and other polygons inscribed in curves. Professor Abram’s Math 383 class, Washington & Lee University.

Fall 2019 Karen Uhlenbeck, 2019 Abel Prize winner (1.8MB) given at the Nobel Prize Symposium, Washington & Lee University.

Winter 2018 The Many ways to knot a tie (1.8MB) given at the Pi Mu Epsilon induction ceremony, Mathematics Department, Washington & Lee University.

Summer 2016 Folded Ribbons Knots in the Plane (4MB) given at Unknot Conference III at Dennison University.

Winter 2014 Cuts & Folds: mathematics & origami (484KB) given at the Pi Mu Epsilon induction ceremony, Mathematics Department, Washington & Lee University.

Spring 2012 Squares and other polygons inscribed in curves (1.1MB). Mathematics Colloquium Wellesley College, Wellesley MA.

October 2009 Introduction to Geometric Knot Theory (2.1MB) Mathematics Colloquium, Connecticut State University.

July 2009 How much string does it take to tie your shoelaces, a talk given at the Hampshire College Summer Studies in Mathematics, Hampshire College and at the Unknot Conference I, Denison University OH.