Matthew R. Ballard

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

For the Spring 2024 semester, I am a Research Professor in the Noncommutative Algebraic Geometry program at SLMath.

I study categorical structures 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 in geometry and arithmetic. I am also interested in formal verification, particularly of modern mathematics.

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

I recently joined the maintainer group for Mathlib, the expansive library of mathematics formalized in the Lean programming language. I always welcome a chat about how formalization, particularly Lean, can make your life better in the age of AI.

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 DMS-2302263 and the Simons Foundation Award 708132. The work has also benefited from a membership at the Institute for Advanced Study and past funding from the NSF, the Simons Foundation, USC, and the Southeastern Conference.

selected publications

  1. arXiv
    High Frobenius pushforwards generate the bounded derived category
    Ballard, Matthew R., Iyengar, Srikanth B., Lank, Pat, Mukhopadhyay, Alapan, and Pollitz, Josh
  2. J. NC Geo.
    Kernels for noncommutative projective schemes
    Ballard, Matthew, and Farman, Blake
    J. Noncommut. Geom. 2021
  3. Ann. K-Theory
    On derived categories of arithmetic toric varieties
    Ballard, Matthew, Duncan, Alexander, and McFaddin, Patrick
    Ann. K-Theory 2019
  4. Crelle
    Variation of geometric invariant theory quotients and derived categories
    Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
    J. Reine Angew. Math. 2019
  5. 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
  6. Invent. Math.
    Orlov spectra: bounds and gaps
    Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
    Invent. Math. 2012