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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, S. Das, C. Wolf, and Y. Yang. Computability of topological pressure on compact shift spaces beyond finite type. Nonlinearity,
  • M. Burr and A. Leykin. Inflation of poorly conditioned zeros of systems of analytic functions. Arnold Mathematical Journal, 2021. arXiv AMJ
  • M. Burr and C. Wolf. Computability at Zero Temperature. Nonlinearity, 2020. arXiv Nonlinearity
  • 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 44th ISSAC
  • 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. 40(2), 367-401, 2020. 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: