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

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

Research

Publications

  1. A sharp bound for hypergeometric rank in dimension three
    with María Cruz Fernández Fernández,
    preprint, 8 pages.
  2. 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.
  3. 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.
  4. 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.
  5. The characteristic cycle and Gevrey solutions of a hypergeometric system
    with María Cruz Fernández Fernández,
    Algebra Number Theory, 14 (2020), no. 2, 323--347.
  6. On normalized Horn systems
    with Laura Felicia Matusevich and Uli Walther
    Collectanea Mathematica, 71 (2), 279--286.
  7. Virtual resolutions for a product of projective spaces
    with Daniel Erman and Gregory G. Smith,
    Algebraic Geometry, 7 (4) (2020) 460--481.
  8. Torus equivariant D-modules and hypergeometric systems
    with Laura Felicia Matusevich and Uli Walther,
    Advances in Mathematics, 350 (2019), 1226--1266.
  9. 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.
  10. Hypergeometric Functions for Projective Toric Curves
    with Jens Forsgård and Laura Felicia Matusevich,
    Advances in Mathematics, 300 (2016), 835--867.
  11. Singularities of binomial D-modules
    with Laura Felicia Matusevich and Uli Walther,
    Journal of Algebra, 439 (2015), 360--372.
  12. Systems of parameters and holonomicity of A-hypergeometric systems
    with Stephen Griffeth and Ezra Miller,
    Pacific Journal of Mathematics, 276-2, (2015), 281--286.
  13. 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.
  14. Euler--Mellin integrals and multivariate hypergeometric functions
    with Jens Forsgård and Mikael Passare,
    Michigan Mathematical Journal, 63, no. 1, 101--123.
  15. 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.
  16. Three flavors of extremal Betti tables
    with Daniel Erman and Manoj Kummini,
    Commutative Algebra, Springer, ed. Irena Peeva (2013), 99--122.
  17. Poset structures in Boij--Söderberg theory
    with Daniel Erman, Manoj Kummini, and Steven V Sam,
    International Mathematics Research Notices (2012), vol. 2012, 5132--5160.
  18. 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.
  19. 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.
  20. The rank of a hypergeometric system
    Compositio Mathematica, 147 (2011), no. 1, 284--318.
  21. Algorithms for Bernstein--Sato polynomials and multiplier ideals
    with Anton Leykin,
    ISSAC 2010.
  22. 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

Postdoc


Graduate student

Teaching

Spring 2023

Math4471W   Mathematics for Social Justice

Fall 2022

Math4281   Introduction to Modern Algebra

Spring 2022

Math5490   Undergraduate Topics: Mathematics for Social Justice (developed new course)

Spring 2021

Math 8202   General Algebra II

Fall 2020

Math8201   General Algebra I

Spring 2020

Math 4281   Introduction to Modern Algebra

Spring 2019

Math 8202   General Algebra

Fall 2018

Math 8201   General Algebra
Math 8300   Topics

Spring 2018

Math 8212   Commutative and Homological Algebra
Math 5385   Introduction to Computational Algebraic Geometry

Fall 2017

Math 8211   Commutative and Homological Algebra

Spring 2017

Math 8202   General Algebra

Fall 2016

Math 4281  Introduction to Modern Algebra
Math 8201   General Algebra

Spring 2016

Math 1271   Calculus I

Spring 2015

Math 8212   Commutative and Homological Algebra

Fall 2014

Math 8211   Commutative and Homological Algebra

Spring 2014

Math 4281   Introduction to Modern Algebra

Fall 2013

Math 4281   Introduction to Modern Algebra

Organizing

CA+

This mini-conference is hosted jointly by Iowa State, Minnesota, and Wisconsin and highlights work in commutative algebra and related fields like algebraic geometry, number theory, combinatorics, and more.

Roots of Unity Workshop

This recurring week-long workshop is designed to support women, particularly women of color, who are in years 1–3 of graduate school and are considering research in algebra, combinatorics, geometry, topology, or number theory.

GEMS in Commutative Algebra

A follow-up to an April 2019 workshop,

Macaulay2 Workshop and Mini-school

A meeting of Macaulay2 developers, including a graduate student mini-school.

Open Problems in Algebraic Combinatorics 2022

At UMN in May 2022, we aired fresh perspectives and open problems in combinatorics and algebra, those that will likely be important for the future.

International Conference on Local Cohomology

A 2017 meeting in honor of Gennady Lyubeznik's 60th birthday.

UMN Commutative Algebra seminar

Mentoring

UMN Gender Minorities In Mathematics (GeMM)

I am the faculty advisor for this active, inspiring group of students! This AWM chapter aims to encourage women and non-binary folks to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equitable treatment of gender minorities in the mathematical sciences at the University of Minnesota.

EDGE Minnesota Mentoring Cluster

I am the leader for this regional mentor group. The EDGE program is designed to strengthen the ability of women and minority students to successfully complete graduate programs in the mathematical sciences.

REU

UMN Combinatorics and Algebra REU

I was the 2019 coordinator for the UMN Combinatorics and Algebra REU and have continued involvement since 2018. This is funded by the NSF through our RTG in Combinatorics and Algebra Grant.

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