Preprints

The order of the articles follows the reverse chronological order in which the preprint was posted.

  1. Rigid homotopies for sampling from algebraic varieties: a Waring structure complexity model (with A. R. Jones & J. I. Rodriguez)
    preprint.
  2. Certifying Galois/monodromy actions via homotopy graphs (with T. Duff)
    preprint.
    (GitHub repo)
  3. Asymptotic rank bounds: a numerical census
    preprint.
    (slides)
  4. A priori bounds for certified Krawczyk homotopy tracking
    preprint (Accepted at MEGA 2026 for presentation).

Publications

  1. Certified surface approximations using the interval Krawczyk test (with M. Burr & J. D. Hauenstein)
    Accepted for the Proceedings of the ISSAC 2026.
  2. Certified algebraic curve projections by path tracking (with M. Burr & M. Byrd)
    In Proceedings of the ISSAC 2025. (2025) pp 87-96.
    (slides), (arxiv)
  3. The tropical variety of symmetric rank 2 matrices (with M. Cai & J. Yu)
    Linear Algebra and its Applications. 720 (1) (2025) pp 50-71.
    (slides), (video), (arxiv)
  4. Effective alpha theory certification using interval arithmetic: alpha theory over regions
    Lecture Notes in Computer Science (In Proceedings of the ICMS 2024). 14749 (2024) pp 275-284.
    (arxiv)
  5. Certified homotopy tracking using the Krawczyk method (with T. Duff)
    In Proceedings of the ISSAC 2024. (2024) pp 274-282.
    (slides), (video), (arxiv)
  6. Implementing real polyhedral homotopy (with J. Lindberg & J. I. Rodriguez)
    Journal of Software for Algebra and Geometry. 14 (1) (2024) pp 59-71.
    (GitHub repo), (arxiv)
  7. Two-step Newton's method for deflation-one singular zeros of analytic systems (with N. Li & L. Zhi)
    Journal of Symbolic Computation. 123 (2024) 102278.
    (arxiv)
  8. Isolating clusters of zeros of analytic systems using arbitrary-degree inflation (with M. Burr & A. Leykin)
    In Proceedings of the ISSAC 2023. (2023) pp 126-134.
    (slides), (arxiv)
  9. On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials (with X. Tang)
    Journal of Scientific Computing. 95 (1) (2023) no. 13.
    (slides), (video), (arxiv)
  10. Homotopy techniques for analytic combinatorics in several variables (with S. Melczer & J. Smolčić)
    In Proceedings of the SYNASC 2022. (2022) pp 27–34.
    (GitHub repo), (slides), (arxiv)
  11. Typical ranks in symmetric matrix completion (with D. I. Bernstein & G. Blekherman)
    Journal of Pure and Applied Algebra. 225 (2021) no. 7, 106603.
    (poster), (arxiv)
  12. Certifying approximate solutions to polynomial systems on Macaulay2
    ACM Communications in Computer Algebra. 53 (2019) no. 2, pp 45–48.
    (software), (slides)
  13. Effective certification of approximate solutions to systems of equations involving analytic functions (with M. Burr & A. Leykin)
    In Proceedings of the ISSAC 2019. (2019) pp 267–274.
    (GitHub repo), (poster), (slides), (arxiv)
  14. Solving polynomial systems via homotopy continuation and monodromy (with T. Duff, C. Hill, A. N. Jensen, A. Leykin & J. Sommars)
    IMA Journal of Numerical Analysis. 39 (2019) no. 3, pp 1421–1446.
    (arxiv)
  15. The dimension of magic squares over fields of characteristics two and three (with W. Jung, J. L. Kim & Y. Kim)
    Linear Algebra and its Applications. 472 (2015) pp 118-134.

Thesis

Thesis: Finding and certifying numerical roots of systems of equations.