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I've run a couple undergraduate research projects (sponsored by NSF funding and internal grant funding). If you are an undergraduate interested in doing one of these, here are some resources to give you a sense of the projects that I've done with students in the past and to give you some ideas of the types of topics my research involves.
Topological Data Analysis (TDA)
Topological Data Analysis (TDA)
In Spring 2022, I mentored an interdisciplinary undergraduate research project on topological data analysis, where the students learned about homology, Betti numbers and persistent homology, and I got to learn about ant colony interaction networks. See the students' poster here.
Scissors Congruence
Scissors Congruence
One of my research projects involves looking at cut and paste invariants of manifolds via algebraic K-theory. While the full machinery behind this uses more complicated category-theoretic tools, there are questions about the structure (such as equivariance under a group action) in lower dimensions that could be appropriate for an undergraduate research project.
Category Theory and Higher Symmetries
Category Theory and Higher Symmetries
In Spring 2024, I mentored an undergraduate independent study on categories, 2-groups and higher symmetries. See these students' poster here.
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