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Research

Research Interests

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

Publications

Preprints

  • M. Burr, E. Rafalin, and D. Souvaine. Dynamic maintenance of half-space depth for points and contours.
    (arXiv, preliminary version 14th FWCG)
  • D. Lipman, M. Burr. Quadratic Generated Normal Domains From Graphs.
    (arXiv)

Journal Publications

  • 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)
  • 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)
  • 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

  • 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.
    (INFORMS)

Author Locators

Students

Ph.D. Students

  • Drew Lipman

MS Students

  • Vito Capuano, “Polygon Distances with Applications to High Performance Liquid Chromatography”
  • Robert Fabrizio
  • Andrew Pitman
  • Alan Hahn

Undergraduate Student Projects

  • Jacob Maggio, “Newton’s method on graphical processing units”
  • Robert Fabrizio, “Uniform Convergence Rates for Halfspace Depth”
  • Andrew Pitman
  • Joseph Bonitati