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Research Interests

  • Algebraic geometry
  • Computational geometry
  • Discrete geometry
  • Symbolic algebra
  • Algorithms
  • Subdivision algorithms
  • Variety approximation


Research 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). Simons Foundation. Collaborations between algebraic geometry and computer science. (2013-2018).

Conference Grants

  • M. Burr (PI), with W. Goddard (co-PI), and S. Poznanovió (co-PI). National Security Agency. 2018 and 2019 Clemson mini-conference on discrete mathemaics and algorithms. (2018-2020).
  • M. Burr (co-PI), with N. Calkin (co-PI), W. Goddard (PI), and S. Poznanovió (co-PI). National Security Agency. 2016 and 2017 Clemson mini-conference on discrete mathematics and algorithms. (2016-2018).



  • M. Burr, E. Rafalin, and D. Souvaine. Dynamic maintenance of half-space depth for points and contours.
    (arXiv, preliminary version 14th FWCG)
  • M. Burr and C. Wolf. Computability at Zero Temperature.

Journal Publications

  • M. Burr, S. Gao, and E. Tsigaridas. The Complexity of Subdivision for Diameter-Distance Tests. Journal of Symbolic Computation. 1-27, 2019.
    (JSC, preliminary version arXiv, preliminary version 42nd ISSAC)
  • M. Burr, S. Gao, and F. Knoll. Optimal Bounds for Johnson-Lindenstrauss Transformations. Journal of Machine Learning Research. 19(73), 1-22, 2018.
    (JMLR, preliminary version arXiv)
  • M.Burr and D. Lipman. Quadratic-Monomial Generated Domains from Mixed Signed, Directed Graphs. International Journal of Algebra and Computation. 2018.
    (IJAC, preliminary version part 1 arXiv, preliminary version part 2 arXiv)
  • M. Burr, M. Schmoll, and C. Wolf. On the computability of rotation sets and their entropies. Ergodic Theory and Dynamical Systems. 2018.
    (ETDS, preliminary version arXiv)
  • M. Burr and R. Fabrizio. Uniform Convergence Rates for Halfspace Depth. Statistics & Probability Letters. 124, 33-40, 2017.
    (SPL, preliminary version arXiv)
  • M. Burr. Continuous amortization and extensions: With applications to bisection-based root isolation. Journal of Symbolic Computation. 77, 78-126, 2016.
    (JSC, preliminary version arXiv)
  • 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.
    (CEJM, preliminary version arXiv)
  • M. Burr and F. Krahmer. SqFreeEVAL: an almost optimal real-root isolation algorithm. Journal of Symbolic Computation. 47(2), 131-152, 2012.
    (JSC, preliminary version with C. Yap ECCC)
  • 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.
    (JSC, preliminary version ISSAC 2008, preliminary version with F. Krahmer 21st FWCG)
  • T. Abbott, M. Burr, M. Chan, E. Demaine, M. Demaine, J. Hugg, D. Kane, S. Langerman, J. Nelson, E. Rafalin, K. Seyboth, V. Yeung. Dynamic ham-sandwich cuts in the plane. Computational Geometry: Theory and Applications. 42(5), 419-428, 2009.
    (CGTA, preliminary version with D. Souvaine 15th FWCG)
  • M. Burr, E. Rafalin, and D. Souvaine. Simplicial depth: an improved definition, analysis, and efficiency for the finite sample case. In R. Liu, R. Serfling, D. Souvaine, editors, Data Depth: Robust Multivariate Analysis, Computational Geometry, and Applications, volume 72 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 195-209. American Mathematical Society, 2006.
    (DIMACS, preliminary version 16th CCCG)
  • M. Burr, A. Cheng, R. Coleman, and D. Souvaine. An intuitive approach to measuring protein surface curvature. PROTEINS: Struture, Function, and Bioinformatics. 61, 1068-1074, 2005.
    (PROTEINS, preliminary version 16th CCCG)

Conference Publications (without journal versions)

  • 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.
  • 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, A. Lauric, and K. Mann. Searching for the center of an ellipse. In Proceedings of the 17th Canadian Conference on Computational Geometry. 260-263, 2005.
    (17th CCCG)
  • M. Burr and D. Letscher. Guaranteed Quality Approximations for Medial Axis of Implicit Planar Curves. In Proceedings of the 24th Fall Workshop on Computational Geometry, 2014.
    (24th FWCG)

Book Reviews

  • M. Burr. Review of Modern Computer Algebra by Joachim von zur Gathen and Jrgen Gerhard. INFORMS Journal on Computing. 27(1), 189-191, 2015.

Author Locators


Ph.D. Students

  • Drew Lipman, “Normal Domains arising from Graph Theory” (2017)

MS Students

  • Vito Capuano, “Polygon Distances with Applications to High Performance Liquid Chromatography” (2015)
  • Andrew Pitman
  • Margaret Brooks, “Threadable Polygonal Chains” (2019)
  • Zachary Johnston, “The Stiefel-Whitney Characteristic Classes” (2019)

Undergraduate Student Projects

  • Jacob Maggio, “Newton’s method on graphical processing units (2013)
  • Robert Fabrizio, “Uniform Convergence Rates for Halfspace Depth” (2016)
  • Andrew Pitman, “Computing Halfspace Depth Dynamically with Red-Black Trees” (2017)
  • Joseph Bonitati, “Halfspace Similarity: Properties and Computation” (2018)