About Me

I work on homological questions about structure resulting from a group action. When a group acts on an algebraic variety, the combinatorics of the orbit structure and induced grading on the structure sheaf shed light on the geometry of the variety, by providing more tools for computing important algebro-geometric invariants.

Contact Info

Christine Berkesch
School of Mathematics, Office 254
University of Minnesota
206 Church Street SE
Minneapolis, MN 55455
cberkesc@umn.edu

Download CV

I am a firm believer in
Federico Ardila's Axioms of Mathematics.

Research

Publications

  1. King's Conjecture and Birational Geometry
    with Matthew Ballard, Michael Brown, Lauren Cranton Heller, Daniel Erman, David Favero, Sheel Ganatra, Andrew Hanlon, Jesse Huang,
    preprint, 56 pages.
  2. On virtual resolutions of points in a product of projective spaces
    with Isidora Bailly-Hall, Karina Dovgodko, Sean Guan, Saisudharshan Sivakumar, Jishi Sun,
    preprint, 21 pages.
  3. A sharp bound for hypergeometric rank in dimension three
    with María Cruz Fernández Fernández,
    Selecta Math. (N.S.), 30 (2024), no. 5, Paper No. 91.
  4. Differential operators, retracts, and toric face rings
    with C-Y. Jean Chan, Patricia Klein, Laura Felicia Matusevich, Janet Page, Janet Vassilev,
    Algebra Number Theory, 17 (2023), no. 11, 1959--1984.
  5. On the rank of an A-hypergeometric D-module vs. the normalized volume of A
    with María Cruz Fernández Fernández,
    Bulletin of the London Mathematical Society, 54 (2022), no. 1, 182--192.
  6. Homological and combinatorial aspects of virtually Cohen--Macaulay sheaves
    with Patricia Klein, Michael C. Loper, and Jay Yang,
    Transactions of the London Mathematical Society, 8 (2021), no. 1, 413--434.
  7. An illustrated view of differential operators on quotients of affine semigroup rings
    with C-Y. Jean Chan, Patricia Klein, Laura Felicia Matusevich, Janet Page, Janet Vassilev,
    Women Math. Ser., 29, Springer, 2021.
  8. The characteristic cycle and Gevrey solutions of a hypergeometric system
    with María Cruz Fernández Fernández,
    Algebra Number Theory, 14 (2020), no. 2, 323--347.
  9. On normalized Horn systems
    with Laura Felicia Matusevich and Uli Walther
    Collectanea Mathematica, 71 (2), 279--286.
  10. Virtual resolutions for a product of projective spaces
    with Daniel Erman and Gregory G. Smith,
    Algebraic Geometry, 7 (4) (2020) 460--481.
  11. Torus equivariant D-modules and hypergeometric systems
    with Laura Felicia Matusevich and Uli Walther,
    Advances in Mathematics, 350 (2019), 1226--1266.
  12. On the parametric behavior of A-hypergeometric series
    with Jens Forsgård and Laura Felicia Matusevich,
    Transactions of the AMS, 370 (2018), no. 6, 4089--4109.
  13. Hypergeometric Functions for Projective Toric Curves
    with Jens Forsgård and Laura Felicia Matusevich,
    Advances in Mathematics, 300 (2016), 835--867.
  14. Singularities of binomial D-modules
    with Laura Felicia Matusevich and Uli Walther,
    Journal of Algebra, 439 (2015), 360--372.
  15. Systems of parameters and holonomicity of A-hypergeometric systems
    with Stephen Griffeth and Ezra Miller,
    Pacific Journal of Mathematics, 276-2, (2015), 281--286.
  16. Jack polynomials as fractional quantum Hall states and the Betti numbers of the (k+1)-equals ideal
    with Stephen Griffeth and Steven V Sam,
    Communications in Mathematical Physics, 330 (2014), no. 1, pp. 415--434.
  17. Euler--Mellin integrals and multivariate hypergeometric functions
    with Jens Forsgård and Mikael Passare,
    Michigan Mathematical Journal, 63, no. 1, 101--123.
  18. Tensor complexes: Multilinear free resolutions constructed from higher tensors
    with Daniel Erman, Manoj Kummini, and Steven V Sam,
    Journal of the European Mathematical Society, 15 (2013), no. 6, 2257--2295.
  19. Three flavors of extremal Betti tables
    with Daniel Erman and Manoj Kummini,
    Commutative Algebra, Springer, ed. Irena Peeva (2013), 99--122.
  20. Poset structures in Boij--Söderberg theory
    with Daniel Erman, Manoj Kummini, and Steven V Sam,
    International Mathematics Research Notices (2012), vol. 2012, 5132--5160.
  21. Shapes of free resolutions over a local ring
    with Daniel Erman, Manoj Kummini, and Steven V Sam,
    Mathematische Annalen, 354 (2012), no. 3, 939--954.
  22. The cone of Betti diagrams over a hypersurface ring of low embedding dimension
    with Jesse Burke, Daniel Erman, and Courtney Gibbons,
    Journal of Pure and Applied Algebra, 216 (2012), 2256--2268.
  23. The rank of a hypergeometric system
    Compositio Mathematica, 147 (2011), no. 1, 284--318.
  24. Algorithms for Bernstein--Sato polynomials and multiplier ideals
    with Anton Leykin,
    ISSAC 2010.
  25. A-graded methods for monomial ideals
    with Laura Felicia Matusevich,
    Journal of Algebra, 322 (2009), 2886--2904.

Conference publications

  1. Combinatorial aspects of virtually Cohen--Macaulay sheaves
    with Patricia Klein, Michael C. Loper, and Jay Yang
    (Proc. FPSAC 2021) Sém. Lothar. Combin., 85B (2021), Art. 63, 13 pp.
  2. The geometry of toric syzygies
    The Notices of the AMS, April (2019). Reprinted April 2022.
  3. Constructing virtual resolutions
    Oberwolfach Report, 43 (2019), 2679--2681.
  4. Free complexes on smooth toric varieties
    Oberwolfach Report, 57 (2016).
  5. Syzygies, finite length modules, and random curves
    with Frank-Olaf Schreyer,
    Commutative Algebra and Noncommutative Algebraic Geometry,
    MSRI Publications (2015), vol. 1, 25--52.
  6. Boij--Söderberg theory and tensor complexes
    Oberwolfach Report, 25 (2013).

Advising

Postdocs


Grad students


Advising Weekly Reports

Teaching

I have taught a variety of courses at all levels at UMN, and I am happy to discuss and swap/share course materials. Currently, our courses operate through Canvas.

Organizing

UMN Commutative Algebra and Algebraic Geometry seminar

CA+

Roots of Unity Workshop

GEMS in Commutative Algebra

Macaulay2 Workshop and Mini-school

Open Problems in Algebraic Combinatorics 2022

International Conference on Local Cohomology

Mentoring

UMN Gender Minorities In Mathematics (GeMM)

EDGE Minnesota Mentoring Cluster

Quotations

  • God used beautiful mathematics in creating the world.

    Paul Dirac

  • 'Obvious' is the most dangerous word in mathematics.

    E. T. Bell

  • Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

    David Hilbert

  • May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.

    James Joseph Sylvester

  • Do not worry too much about your difficulty in mathematics, I can assure you that mine are still greater.

    Albert Einstein