Research
My interests center around the study of the derived category of a variety and its applications to other subfields of algebraic geometry, such as birational geometry and moduli theory. I am also interested in the noncommutative and higher-algebraic structures which arise in these contexts (Calabi-Yau structures, A infinity, etc.).
I am currently thinking about a handful of things, namely derived categories of singular varieties, singularity categories and analogues of matrix factorizations for non-complete intersection singularities, Bridgeland stability conditions, and semiorthogonal decompositions of surfaces.
While not strictly research, I often write notes for myself whenever there is an interesting topics course, try to learn a new topic, or run a seminar. While many are in too poor a form to be read, some of the more readable ones can be found if you click here. Of course, the usual warning is that I claim no originality in any of these, and any errors are my own. I have not spent much time checking for typos and mathematical errors, so reader beware.
Papers
- A note on semiorthogonal indecomposability of some Cohen-Macaulay varieties. Journal of Pure and Applied Algebra, Volume 226, 2022, https://doi.org/10.1016/j.jpaa.2022.107076.
- Reconstruction of projective curves from the derived category. Michigan Math. J. Advance Publication 1 - 24, 2021. https://doi.org/10.1307/mmj/20205910.
- An explicit derived McKay correspondence for some complex reflection groups of rank two. with A. Bhapuri, Y. Davidov, E. Faber, K. Honigs, P. McDonald, and C. E. Overton-Walker. In preparation.
Other Writing
- Boundedness of semistable sheaves. with H. Guo, S. Shivaprasad, and Y. Wu. Published in the London Mathematical Society Lecture Note Series.