publications

Published articles and preprints.

2025

  1. LNAI
    Growing Mathlib: maintenance of a large scale mathematical library
    Ballard, Matthew Robert, Baanen, Anne, Commelin, Johan, Chen, Bryan Gin-ge, Rothgang, Michael, and Testa, Damiano
    In Lecture Notes in Artificial Intelligence 2025
  2. arXiv
    King’s Conjecture and the Cox category
    Ballard, Matthew R., Berkesch, Christine, Brown, Michael K., Cranton Heller, Lauren, Erman, Daniel, Favero, David, Ganatra, Sheel, Hanlon, Andrew, and Huang, Jesse
    2025

2024

  1. Adv. Math.
    Separable algebras and coflasque resolutions
    Ballard, Matthew R., Duncan, Alexander, Lamarche, Alicia, and McFaddin, Patrick K.
    Advances in Mathematics 2024

2023

    2022

    1. Math. Nach.
      Derived categories of centrally-symmetric smooth toric Fano varieties
      Ballard, Matthew R., Duncan, Alexander, and McFaddin, Patrick K.
      Mathematische Nachrichten 2022

    2021

    1. J. NC Geo.
      Kernels for noncommutative projective schemes
      Ballard, Matthew, and Farman, Blake
      J. Noncommut. Geom. 2021
    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

    2020

    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

    2019

    1. Eur. J. Math.
      The toric Frobenius morphism and a conjecture of Orlov
      Ballard, Matthew R., Duncan, Alexander, and McFaddin, Patrick K.
      Eur. J. Math. 2019
    2. Ann. K-Theory
      On derived categories of arithmetic toric varieties
      Ballard, Matthew, Duncan, Alexander, and McFaddin, Patrick
      Ann. K-Theory 2019
    3. Crelle
      Variation of geometric invariant theory quotients and derived categories
      Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
      J. Reine Angew. Math. 2019

    2018

    1. Superschool on derived categories and D-branes
      2018
    2. Math. Ann.
      On the derived categories of degree d hypersurface fibrations
      Ballard, Matthew, Deliu, Dragos, Favero, David, Isik, M. Umut, and Katzarkov, Ludmil
      Math. Ann. 2018

    2017

    1. arXiv
      Kernels from compactifications
      Ballard, Matthew R., Diemer, Colin, and Favero, David
      2017
    2. Alg. Geo.
      Wall crossing for derived categories of moduli spaces of sheaves on rational surfaces
      Ballard, Matthew Robert
      Algebr. Geom. 2017
    3. JEMS
      Homological projective duality via variation of geometric invariant theory quotients
      Ballard, Matthew, Deliu, Dragos, Favero, David, Isik, M. Umut, and Katzarkov, Ludmil
      J. Eur. Math. Soc. (JEMS) 2017

    2016

    1. Adv. Math.
      Resolutions in factorization categories
      Ballard, Matthew, Deliu, Dragos, Favero, David, Isik, M. Umut, and Katzarkov, Ludmil
      Adv. Math. 2016

    2015

    1. Trans. AMS
      The Mori program and non-Fano toric homological mirror symmetry
      Ballard, Matthew, Diemer, Colin, Favero, David, Katzarkov, Ludmil, and Kerr, Gabriel
      Trans. Amer. Math. Soc. 2015

    2014

    1. 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
    2. JMPA
      A category of kernels for equivariant factorizations, II: further implications
      Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
      J. Math. Pures Appl. (9) 2014

    2012

    1. Invent. Math.
      Orlov spectra: bounds and gaps
      Ballard, Matthew, Favero, David, and Katzarkov, Ludmil
      Invent. Math. 2012
    2. IMRN
      Hochschild dimensions of tilting objects
      Ballard, Matthew, and Favero, David
      Int. Math. Res. Not. IMRN 2012

    2011

    1. Adv. Math.
      Derived categories of sheaves on singular schemes with an application to reconstruction
      Ballard, Matthew Robert
      Adv. Math. 2011

    2009

    1. arXiv
      Equivalences of derived categories of sheaves on quasi-projective schemes
      Ballard, Matthew Robert
      2009

    2008

    1. arXiv
      Sheaves on local Calabi-Yau varieties
      Ballard, Matthew Robert
      2008
    2. Thesis
      Derived categories of sheaves of quasi-projective schemes
      Ballard, Matthew Robert
      2008
    3. Meet homological mirror symmetry
      Ballard, Matthew Robert
      2008