My work focuses on understanding Adams operations for the Burnside ring, specifically if they naturally factor through the power operation. Currently, I've answered this question for abelian groups, and am working to expand this to broader classes of groups.
I've also been working with the University of Kentucky Bourbon Seminar on exponential operations in cohomology theories. Nathaniel Stapleton recently gave a talk regarding our work at the Northwestern Topology Conference in honor of Paul Goerss.
You may find a link to my research statement here.
Papers
- There is an upcoming UKY Bourbon Seminar paper, not yet posted to arXiv.
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Undergraduate Research
- I work with the UKY Mathlab to assist in 3d printing models for visualization and to maintain the 3d printers. I'm currently training a graduate student to for this position once I graduate and recruiting an undergraduate student to work with them.
- In Summer 2022, I supervised an undergraduate research group which studied a functor between commutative rings and categories.
People
Here are some of my collaborators:
Nathaniel Stapleton, David Mehrle, Davis Deaton, Shahzad Kalloo, Nathan Cornelius.