I am a PhD student at LSU working under the supervision of Dr. Milen Yakimov. My research interests are at the intersection of algebraic categorification, noncommutative algebra, representation theory, and tensor-triangular geometry. Specifically, I am interested in:
- noncommutative analogues of Balmer's prime spectrum of a tensor-triangulated category;
- the role of the different categorical prime spectra in the context of algebraic categorification of noncommutative algebras, including how new categorifications can be produced using prime spectra;
- the role of the different categorical prime spectra in the context of derived categories of non-braided monoidal abelian categories, such as the category of bimodules for a noncommutative algebra.
An arxiv preprint of some of this work is available here
I did my Master's degree at Wake Forest University under the supervision of Dr. Ellen Kirkman
, and my Master's thesis
was in the area of noncommutative invariant theory, in particular the study of dual reflection groups, which arise in the search for a noncommutative version of the classical Shephard-Todd-Chevalley Theorem.