Matthew R. Ballard

Currently faculty in the Department of Mathematics at UofSC 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.

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.

funding

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.

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 √Čtudes Sci. 2014
  5. Invent. Math.
    Orlov spectra: bounds and gaps
    Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
    Invent. Math. 2012