Matthew R. Ballard

Professor in the Department of Mathematics at USC and a member of the SC AG NT group.

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 more information about me, see my CV. For a list of my papers, please view the publications page.

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.

news

Sep 24, 2023 Ballard joins Mathlib maintainers
Sep 1, 2023 Ballard awarded an NSF grant
Mar 31, 2023 New Arxiv preprint
Sep 1, 2022 VandeBogert awarded an NSF DMS postdoc
Aug 31, 2022 AMS MRC applications open

funding

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.

selected publications

  1. arXiv
    Consequences of the existence of exceptional collections in arithmetic and rationality
    Ballard, Matthew R., Duncan, Alexander, Lamarche, Alicia, and McFaddin, Patrick K
    2020
  2. JMPA
    Kernels for Grassmann flops
    Ballard, Matthew R., Chidambaram, Nitin K., Favero, David, McFaddin, Patrick K., and Vandermolen, Robert R.
    J. Math. Pures Appl. (9) 2021
  3. Crelle
    Variation of geometric invariant theory quotients and derived categories
    Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
    J. Reine Angew. Math. 2019
  4. Pub. IHES
    A category of kernels for equivariant factorizations and its implications for Hodge theory
    Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
    Publ. Math. Inst. Hautes Études Sci. 2014
  5. Invent. Math.
    Orlov spectra: bounds and gaps
    Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
    Invent. Math. 2012