I study algebraic geometry and am particularly interested in questions arising from mirror symmetry. Much of my current work focuses on derived categories and their relation to more classical questions. I am also interested in formal verification, particular of modern mathematics.
For a little of my pedagogical philosophy and experience, see my teaching page. As an extension of teaching, I take pride in mentoring researchers at all stages and I regularly organize mathematical events, even virtual ones. If you are interested in participating in such an event, please contact me.
Currently, my research is partially supported by the National Science Foundation. It has also been supported by the Simons Foundation. The work has also benefited from a membership at the Institute for Advanced Study and funding from USC and the Southeastern Conference.
- arXivConsequences of the existence of exceptional collections in arithmetic and rationality2020
- JMPAKernels for Grassmann flopsJ. Math. Pures Appl. (9) 2021
- CrelleVariation of geometric invariant theory quotients and derived categoriesJ. Reine Angew. Math. 2019
- Pub. IHESA category of kernels for equivariant factorizations and its implications for Hodge theoryPubl. Math. Inst. Hautes Études Sci. 2014
- Invent. Math.Orlov spectra: bounds and gapsInvent. Math. 2012