I enjoy collaborating with undergraduate students on research, and many of my ongoing projects have aspects that are well-suited for student involvement. Since Spring 2019, I have been involved with the Washington Experimental Mathematics Laboratory (WXML), a program designed to introduce undergraduate students to the mathematical research process.
Here are some slides from a recent talk I gave to students in the UW Applied and Computational Mathematical Sciences program about my experience working on WXML projects.
Along with Fran Herr, Legrand Jones (UW undergraduates) and Rowan Rowlands (UW graduate student), I have recently finished a project started in Fall 2019 on simplicial complexes that arise from matchings on graphs. This project stems in part from a question that my coauthors and I asked in the paper "Manifold matching complexes."
We've split our results into two separate parts. One part of our project studies the behavior of graphs when the matching complex operation is performed multiple times. Fran and Legrand have determined the behavior of graphs for which this process never terminates. Outside of two special graphs (which can be seen as fundamental obstructions to the process terminating), all graphs in this class grow without bound.
The other part of our project characterizes certain graphs whose matching complexes are Buchsbaum, which is a generalization of being a manifold. Fran and Legrand have given numerous talks about our progress, including at the UW Undergraduate Research Symposium and the Young Mathematicians Conference. Our work has resulted in the following papers.
| Iterated matching graphs by Fran Herr and Legrand Jones II. Submitted to the Rose-Hulman Undergraduate Mathematics Journal. |
Preprint |
| A characterization of two-dimensional Buchsbaum matching complexes
Joint with Fran Herr, Legrand Jones II, and Rowan Rowlands. Preprint. |
Preprint |
In Spring 2019, I worked with Maddy Brown, Spencer Kraisler, Zhongyan Wang (UW undergrads), and Amzi Jeffs (UW grad student) on a project called "Powers of higher nerves." Our investigations built off of results from the paper "Higher nerves of simplicial complexes." We investigated a conjecture I made connecting collapsibility and higher nerves, and we wrote SageMath code to compute higher nerves. You can read Maddy, Spencer, and Zhongyan's final report here.
If you're an undergraduate who's interested in working on research with me, please feel free to email me to discuss possible projects.