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Contact Information

  • burr2 (at) clemson (dot) edu
  • 864-656-5220
  • O-19 Martin Hall
    Department of Mathematical Sciences
    Clemson University
    220 Parkway Drive
    Clemson, SC 29634-0975

Research Interests

My research interests include algebraic geometry, computational geometry, symbolic algebra, and applied algebraic geometry.

Current Grants

  • M. Burr (PI). National Science Foundation. Certification Algorithms for Polynomial System Solving (2019-2020).
  • M. Burr (PI). National Science Foundation. AF: Small: Subdivision methods: Correctness and complexity. (2015-2019).
  • M. Burr (PI), with W. Goddard (co-PI), and S. Poznanovi√≥ (co-PI). National Security Agency. 2018 and 2019 Clemson mini-conference on discrete mathemaics and algorithms. (2018-2020).

Recent Publications


  • M. Burr, E. Rafalin, and D. Souvaine. Dynamic maintenance of half-space depth for points and contours. arXiv 14th FWCG

(Recent) Publications

  • M. Burr and C. Wolf. Computability at Zero Temperature. Nonlinearity, 2020. arXiv
  • M. Burr, S. Gao, and E. Tsigaridas. The Complexity of Subdivision for Diameter-Distance Tests. Journal of Symbolic Computation. 101, 1-27, 2020. arXiv 42nd ISSAC JSC
  • M. Burr, K. Lee, and A. Leykin. Effective certification of approximate solutions to systems of equations involving analytic functions. In Proceedings of the 44th International Symposium on Symbolic and Algebraic Computation, 2019. arXiv
  • M. Burr, S. Gao, and F. Knoll. Optimal Bounds for Johnson-Lindenstrauss Transformations. Journal of Machine Learning Research. 19(73), 1-22, 2018. arXiv JMLR
  • M.Burr and D. Lipman. Quadratic-Monomial Generated Domains from Mixed Signed, Directed Graphs. International Journal of Algebra and Computation. 2018. arXiv (Part 1) arXiv (Part 2) IJAC
  • M. Burr, M. Schmoll, and C. Wolf. On the computability of rotation sets and their entropies. Ergodic Theory and Dynamical Systems. 2018. arXiv ETDS
  • J. Xu, M. Burr, and C. Yap. An approach for certifying homotopy continuation paths: Univariate case. In Proceedings of the 43nd International Symposium on Symbolic and Algebraic Computation 399-406, 2018. 43rd ISSAC
  • M. Burr and R. Fabrizio. Uniform Convergence Rates for Halfspace Depth. Statistics & Probability Letters. 124, 33-40, 2017. arXiv SPL
  • M. Burr. Continuous amortization and extensions: With applications to bisection-based root isolation. Journal of Symbolic Computation. 77, 78-126, 2016. arXiv JSC
  • M. Burr. Asymptotic Purity for Very General Hypersurfaces of \mathbb{P}^n\times\mathbb{P}^n of Bidegree (k,k). Central European Journal of Mathematics 10(2), 530-542, 2012. arXiv CEMJ
  • M. Burr and F. Krahmer. SqFreeEVAL: An (Almost) Optimal Real-Root Isolation Algorithm. Journal of Symbolic Computation 47(2), 131-152, 2012. arXiv JSC
  • M. Burr, S. Choi, B. Galehouse, and C. Yap. Complete Subdivision Algorithms II: Isotopic Meshing of General Algebraic Curves. Journal of Symbolic Computation 47(2), 153-166, 2012. arXiv JSC

Current Teaching

I am currently teaching:

  • MATH 3110: Linear Algebra
  • MATH 3190: Introduction to Proof

Research Groups

I am in residence at the semester program on Nonlinear Algebra at the Institute of Computational and Experimental Research in Mathematics.

I am member of the Combinatorics and Discrete Math Group at Clemson University.

I am member of the Applicable and Computational Algebra Lab at Clemson University.

Previously, I was involved with several research groups: