Patricia Klein: Research

Papers and preprints:

The button next to each paper title will display (or hide) the appropriate abstract.
† denotes undergraduate mentee.
  1. On basic double G-links of squarefree monomial ideals (with Matthew Koban† and Jenna Rajchgot) Down Arrow

    Accepted to Journal of Commutative Algebra, 14 pages.
    arXiv:2209.00119
  2. Differential operators, retracts, and toric face rings (with Christine Berkesch, C.-Y. Jean Chan, Laura Felicia Matusevich, Janet Page, and Janet Vassilev) Down Arrow

    Algebra & Number Theory 17 (2023), no. 11, 1959–1984.
    arXiv:2112.00266
  3. Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials (with Anna Weigandt) Down Arrow

    Submitted, 50 pages.
    arXiv:2108.08370
  4. An illustrated view of differential operators of a reduced quotient of an affine semigroup ring (with Christine Berkesch, C.-Y. Jean Chan, Laura Felicia Matusevich, Janet Page, and Janet Vassilev), 2021. Down Arrow

    In: Miller, C., Striuli, J., Witt, E.E. (eds) Women in Commutative Algebra. Association for Women in Mathematics Series, vol 29. Springer, Cham, 49–94.
    arXiv:2105.04074
  5. Homological and combinatorial aspects of virtually Cohen–Macaulay sheaves (with Christine Berkesch, Michael C. Loper, and Jay Yang) Down Arrow

    Transactions of the London Mathematical Society 8 (2021), no. 1, 413–434.
    arXiv:2012.14047
  6. Diagonal degenerations of matrix Schubert varieties Down Arrow

    Algebraic Combinatorics 6 (2023), no. 4, 1073-1094.
    arXiv:2008.01717
  7. Geometric vertex decomposition and liaison (with Jenna Rajchgot) Down Arrow

    Forum of Mathematics, Sigma 9 (2021), e70.
    arXiv:2005.14289
  8. Toric double determinantal varieties (with Alexander Blose†, Owen McGrath†, and Jackson Morris†) Down Arrow

    Communications in Algebra 49 (2021), no. 7, 3085–3093.
    arXiv:2006.04191
  9. Gröbner bases and the Cohen–Macaulay property of Li's double determinantal varieties (with Nathan Fieldsteel) Down Arrow

    Proceedings of the AMS, Series B, 7 (2020), 142–158.
    arXiv:1906.06817
  10. Characterizing finite length local cohomology in terms of bounds on Koszul cohomology Down Arrow

    Journal of Algebra 543 (2020), 198–224.
    arXiv:1810.01359
  11. Lech's inequality, the Stückrad–Vogel conjecture, and uniform behavior of Koszul homology (with Linquan Ma, Phạm Hùng Quý, Ilya Smirnov, and Yongwei Yao) Down Arrow

    Advances in Mathematics 347 (2019), 442–472.
    arXiv:1808.01051




Other writings:



  1. The MatrixSchubert package for Macaulay2 (with Ayah Almousa, Sean Grate, Daoji Huang, Adam LaClair, Yuyuan Luo, and Joseph McDonough)

    This paper accompanies the MatrixSchubert package that we wrote for release in version 1.23 of Macaulay2, which is open source software used for computations in commutative algebra and algebraic geometry.

  2. Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials (with Anna Weigandt)

    FPSAC extended abstract (2022), accepted as talk.

  3. Geometric vertex decomposition and liaison (with Jenna Rajchgot)

    FPSAC extended abstract (2021), accepted as poster.

  4. Combinatorial aspects of virtually Cohen–Macaulay sheaves (with Christine Berkesch, Michael C. Loper, and Jay Yang)

    FPSAC extended abstract (2021), accepted as poster.

  5. Relationships among Hilbert-Samuel multiplicities, Koszul cohomology, and local cohomology

    Thesis, University of Michigan (2018).





  6. I also have a couple of papers in cognitive psychology, from my previous life as an undergraduate with an interest in cognitive science:

    Retrieval attempts enhance learning, but retrieval success (versus failure) does not matter (with Nate Kornell and Katherine Rawson)
    Journal of Experimental Psychology: Learning, Memory, and Cognition, 41(1):283 (2015).


    Tests enhance learning — compared to what? (with Nate Kornell and Veronica Rabelo)
    Journal of Applied Research in Memory and Cognition, 1:259 (2015).