Research

• Symmetric Tropical Rank 2 Matrices (with M. Cai & J. Yu). preprint.
  (slides)
• Effective alpha theory certification using interval arithmetic: alpha theory over regions. Lecture Notes in Computer Science. 14749 (2024) pp 275-284.
  (arxiv)
• 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), (arxiv)
• 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)
• 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)
• 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)
• 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), (arxiv)
• The NumericalCertification package in Macaulay2. preprint.
  (software), (slides)
• 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)
• 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)
• Certifying approximate solutions to polynomial systems on Macaulay2. ACM Communications in Computer Algebra. 53 (2019) no. 2, pp 45–48.
  (software), (slides)
• 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)
• 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)

• 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.