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.
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.
|Sep 1, 2022||VandeBogert awarded an NSF DMS postdoc|
|Aug 31, 2022||AMS MRC applications open|
|Mar 31, 2022||Ballard wins UofSC Garnet Apple for Teaching Innovation|
|Jul 1, 2021||Lamarche awarded an NSF DMS postdoc|
|Jun 22, 2020||Ballard awarded an Simons Foundation grant|
Currently, my research is partially supported by the Simons Foundation. It has also been supported by the National Science Foundation. The work has also benefited from a membership at the Institute for Advanced Study and funding from UofSC 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