Research

1. Certified surface approximations using the interval Krawczyk test (with M. Burr & J. D. Hauenstein)
   preprint.
2. Asymptotic rank bounds: a numerical census
   preprint.
   (slides)
3. A priori bounds for certified Krawczyk homotopy tracking
   preprint.
4. Certified algebraic curve projections by path tracking (with M. Burr & M. Byrd)
   In Proceedings of the 2025 on International Symposium on Symbolic and Algebraic Computation. (2025) pp 87-96.
   (slides), (arxiv)
5. 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)
6. Effective alpha theory certification using interval arithmetic: alpha theory over regions
   Lecture Notes in Computer Science. 14749 (2024) pp 275-284.
   (arxiv)
7. Certified homotopy tracking using the Krawczyk method (with T. Duff)
   In Proceedings of the 2024 on International Symposium on Symbolic and Algebraic Computation. (2024) pp 274-282.
   (slides), (video), (arxiv)
8. 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)
9. Isolating clusters of zeros of analytic systems using arbitrary-degree inflation (with M. Burr & A. Leykin)
   In Proceedings of the 2023 on International Symposium on Symbolic and Algebraic Computation. (2023) pp 126-134.
   (slides), (arxiv)
10. Homotopy techniques for analytic combinatorics in several variables (with S. Melczer & J. Smolčić)
    In Proceedings of International Symposium on Symbolic and Numeric Algorithms for Scientific Computing 2022. (2022) pp 27–34.
    (GitHub repo), (slides), (arxiv)
11. 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)
12. The NumericalCertification package in Macaulay2
    preprint.
    (software), (slides)
13. 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)
14. 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)
15. Certifying approximate solutions to polynomial systems on Macaulay2
    ACM Communications in Computer Algebra. 53 (2019) no. 2, pp 45–48.
    (software), (slides)
16. Effective certification of approximate solutions to systems of equations involving analytic functions (with M. Burr & A. Leykin)
    In Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation. (2019) pp 267–274.
    (GitHub repo), (poster), (slides), (arxiv)
17. 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)

18. 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.