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.
Other Writing
- Boundedness of semistable sheaves. with H. Guo, S. Shivaprasad, and Y. Wu. arXiv 2112.03834 Submitted as part of the Stacks Project Expository Collection (SPEC) to be published in the London Mathematical Society Lecture Note Series.