publications

Published articles and preprints.

2026

  1. Forum Sigma
    High Frobenius pushforwards generate the bounded derived category
    Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank, and 2 more authors
    Forum of Mathematics, Sigma, 2026

2025

  1. LNAI
    Growing Mathlib: maintenance of a large scale mathematical library
    Matthew Robert Ballard, Anne Baanen, Johan Commelin, and 3 more authors
    In Lecture Notes in Artificial Intelligence, 2025
  2. arXiv
    King’s Conjecture and the Cox category
    Matthew R. Ballard, Christine Berkesch, Michael K. Brown, and 6 more authors
    2025

2024

  1. Adv. Math.
    Separable algebras and coflasque resolutions
    Matthew R. Ballard, Alexander Duncan, Alicia Lamarche, and 1 more author
    Advances in Mathematics, 2024
    DOI

2022

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

2021

  1. J. NC Geo.
    Kernels for noncommutative projective schemes
    Matthew Ballard and Blake Farman
    J. Noncommut. Geom., 2021
    DOI
  2. JMPA
    Kernels for Grassmann flops
    Matthew R. Ballard, Nitin K. Chidambaram, David Favero, and 2 more authors
    J. Math. Pures Appl. (9), 2021
    DOI

2020

  1. arXiv
    Consequences of the existence of exceptional collections in arithmetic and rationality
    Matthew R. Ballard, Alexander Duncan, Alicia Lamarche, and 1 more author
    2020

2019

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

2018

  1. Superschool on derived categories and D-branes
    2018
    Edmonton, Canada, July 17–23, 2016, Lectures from the PIMS Superschool
    DOI
  2. Math. Ann.
    On the derived categories of degree d hypersurface fibrations
    Matthew Ballard, Dragos Deliu, David Favero, and 2 more authors
    Math. Ann., 2018
    DOI

2017

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

2016

  1. Adv. Math.
    Resolutions in factorization categories
    Matthew Ballard, Dragos Deliu, David Favero, and 2 more authors
    Adv. Math., 2016
    DOI

2015

  1. Trans. AMS
    The Mori program and non-Fano toric homological mirror symmetry
    Matthew Ballard, Colin Diemer, David Favero, and 2 more authors
    Trans. Amer. Math. Soc., 2015
    DOI

2014

  1. Pub. IHES
    A category of kernels for equivariant factorizations and its implications for Hodge theory
    Matthew Ballard, David Favero, and Ludmil Katzarkov
    Publ. Math. Inst. Hautes Études Sci., 2014
    DOI
  2. JMPA
    A category of kernels for equivariant factorizations, II: further implications
    Matthew Ballard, David Favero, and Ludmil Katzarkov
    J. Math. Pures Appl. (9), 2014
    DOI

2012

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

2011

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

2009

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

2008

  1. arXiv
    Sheaves on local Calabi-Yau varieties
    Matthew Robert Ballard
    2008
  2. Thesis
    Derived categories of sheaves of quasi-projective schemes
    Matthew Robert Ballard
    2008
    Thesis (Ph.D.)–University of Washington
  3. Meet homological mirror symmetry
    Matthew Robert Ballard
    In Modular forms and string duality, 2008