I am a PhD student at LSU working under the supervision of Dr. Milen Yakimov. My research interests are in noncommutative algebra, noncommutative algebraic geometry, and algebraic categorification. Specifically, my current work deals with:
- defining the prime (and completely prime, semiprime, and primitive) spectrum of a 2-category, which is a categorical version of the classical notion of the prime (and completely prime, semiprime, and primitive) spectrum of a noncommutative ring;
- investigating the role of the different categorical prime spectra in the context of algebraic categorification of noncommutative algebras;
- constructing a specific categorification of the quantized coordinate rings of Richardson varieties of arbitrary symmetric Kac-Moody algebras.
An arxiv preprint 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.