## Research

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

## Thesis

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