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Preprints

  1. Jonathan D. Hauenstein and Margaret H. Regan,
    Adaptive strategies for solving parameterized systems using homotopy continuation (pdf, computation page).

  2. Luca Chiantini, Jonathan D. Hauenstein, Christian Ikenmeyer, Giorgio Ottaviani, and J.M. Landsberg,
    Polynomials and the exponent of matrix multiplication (pdf, computation page).

  3. Jonathan D. Hauenstein, Samantha N. Sherman, and Charles W. Wampler,
    Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group (pdf, computation page).

  4. Heather A. Harrington, Dhagash Mehta, Helen M. Byrne, and Jonathan D. Hauenstein,
    Decomposing the parameter space of biological networks via a numerical discriminant approach (pdf, appendix, movie and software).

  5. Daniel A. Brake, Jonathan D. Hauenstein, and Cynthia Vinzant,
    Computing complex and real tropical curves using monodromy (pdf).

  6. Daniel K. Molzahn, Matthew Niemerg, Dhagash Mehta, and Jonathan D. Hauenstein,
    Investigating the maximum number of real solutions to the power flow equations: analysis of loseless four-bus systems (pdf).

  7. Jonathan D. Hauenstein and Jose I. Rodriguez,
    Numerical irreducible decomposition of multiprojective varieties (pdf).

  8. Joseph Cleveland, Jeffrey Dzugan, Jonathan D. Hauenstein, Ian Haywood, Dhagash Mehta, Anthony Morse, Leonardo Robol, and Taylor Schlenk,
    Certified counting of roots of random univariate polynomials (pdf).

  9. Jonathan D. Hauenstein,
    Algebraic computations using Macaulay dual spaces (pdf).

  10. Owen Coss, Jonathan D. Hauenstein, Hoon Hong, and Daniel K. Molzahn,
    Locating and counting equilibria of the Kuramoto model with rank one coupling (pdf, software).
    A version of this article will appear in SIAM Journal on Applied Algebraic Geometry.

  11. Jonathan D. Hauenstein,
    Certification using Newton-invariant subspaces (pdf, computation page).
    A version of this article will appear in Lecture Notes in Computer Science.

  12. Daniel J. Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Homotopies for connected components of algebraic sets with application to computing critical sets (pdf).
    A version of this article will appear in Lecture Notes in Computer Science.

  13. Jonathan D. Hauenstein, Jose I. Rodriguez, and Frank Sottile,
    Numerical computation of Galois groups (pdf).
    A version of this article will appear in Foundations of Computational Mathematics.

  14. Jonathan D. Hauenstein, Luke Oeding, Giorgio Ottaviani, and Andrew J. Sommese,
    Homotopy techniques for tensor decomposition and perfect identifiability (pdf).
    A version of this article will appear in Journal für die reine und angewandte Mathematik.

  15. Tulay Ayyildiz Akoglu, Jonathan D. Hauenstein, and Agnes Szanto,
    Certifying solutions to overdetermined and singular polynomial systems over Q (pdf).
    A version of this article appeared in Journal of Symbolic Computation, 84, 147-171, 2018.

  16. Alessandra Bernardi, Noah S. Daleo, Jonathan D. Hauenstein, and Bernard Mourrain,
    Tensor decomposition and homotopy continuation (pdf, computation page).
    A version of this article appeared in Differential Geometry and its Applications, 55, 78-105, 2017.

  17. Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Algorithm 976: Bertini_real: Numerical decomposition of real algebraic curves and surfaces (pdf).
    A version of this article appeared in ACM Transactions on Mathematical Software, 44(1), 10, 2017.

  18. Jonathan D. Hauenstein, Bernard Mourrain, and Agnes Szanto,
    On deflation and multiplicity structure (pdf).
    A version of this article appeared in Journal of Symbolic Computation, 83, 228-253, 2017.

  19. Adam Mahdi, Claudio Pessoa, and Jonathan D. Hauenstein,
    A hybrid symbolic-numerical approach to the center-focus problem (pdf, homotopy continuation and first integrals (April 2015 at Colorado College)).
    A version of this article appeared in Journal of Symbolic Computation, 82, 57-73, 2017.

  20. Jonathan D. Hauenstein, Charles W. Wampler, and Martin Pfurner,
    Synthesis of three-revolute spatial chains for body guidance (pdf).
    A version of this article appeared in Mechanism and Machine Theory, 110, 61-72, 2017.

  21. Jonathan D. Hauenstein and Viktor Levandovskyy,
    Certifying solutions to square systems of polynomial-exponential equations (pdf, computation page).
    A version of this article appeared in Journal of Symbolic Computation, 79(3), 575-593, 2017.

  22. Jonathan D. Hauenstein and Andrew J. Sommese,
    What is numerical algebraic geometry? (pdf).
    A version of this article appeared in Journal of Symbolic Computation, 79(3), 499-507, 2017.

  23. Jonathan D. Hauenstein and Charles W. Wampler,
    Unification and extension of intersection algorithms in numerical algebraic geometry (pdf, computation page).
    A version of this article appeared in Applied Mathematics and Computation, 293, 226-243, 2017.

  24. Hythem Sidky, Alan C. Liddell, Jr., Dhagash Mehta, Jonathan D. Hauenstein, and Jonathan Whitmer,
    An algebraic geometric method for calculating phase equilibria from fundamental equations of state (pdf).
    A version of this article appeared in Industrial & Engineering Chemistry Research, 55(43), 11363-11370, 2016.

  25. Daniel J. Bates, Jonathan D. Hauenstein, Matthew E. Niemerg, and Frank Sottile,
    Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials (pdf, software).
    A version of this article appeared in Numerical Algorithms, 73(1), 281-304, 2016.

  26. Jonathan D. Hauenstein, Nickolas Hein, and Frank Sottile,
    A primal-dual formulation for certifiable computations in Schubert calculus (pdf).
    A version of this article appeared in Foundations of Computational Mathematics, 16(4), 941-963, 2016.

  27. Daniel A. Brake, Jonathan D. Hauenstein, and Alan C. Liddell,
    Validating the completeness of the real solution set of a system of polynomial equations (pdf).
    A version of this article appeared in Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2016, pp. 143-150.

  28. Fulvio Gesmundo, Jonathan D. Hauenstein, Christian Ikenmeyer, and J.M. Landsberg,
    Complexity of linear circuits and geometry (pdf, computation page).
    A version of this article appeared in Foundations of Computational Mathematics, 16(3), 599-635, 2016.

  29. Daniel A. Brake, Jonathan D. Hauenstein, Andrew P. Murray, David H. Myszka, and Charles W. Wampler,
    The complete solution of Alt-Burmester synthesis problems for four-bar linkages (pdf).
    A version of this article appeared in Journal of Mechanisms and Robotics, 8(4), 041018, 2016.

  30. Noah S. Daleo, Jonathan D. Hauenstein, and Luke Oeding,
    Computations and equations for Segre-Grassmann hypersurfaces (pdf).
    A version of this article appeared in Portugaliae Mathematica, 73(1), 71-90, 2016.

  31. Jonathan D. Hauenstein and Alan C. Liddell, Jr.,
    Certified predictor-corrector tracking for Newton homotopies (pdf).
    A version of this article appeared in Journal of Symbolic Computation, 74, 239-254, 2016.

  32. Noah S. Daleo and Jonathan D. Hauenstein,
    Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme (pdf, computation page).
    A version of this article appeared in Journal of Symbolic Computation, 72, 128-146, 2016.

  33. Jonathan D. Hauenstein and Alan C. Liddell, Jr.,
    A hybrid symbolic-numeric approach to exceptional sets of generically zero-dimensional systems (pdf, computation page).
    A version of this article appeared in Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, ACM, New York, 2015, pp. 53-60.

  34. Jonathan D. Hauenstein, Bernard Mourrain, and Agnes Szanto,
    Certifying isolated singular points and their multiplicity structure (pdf, computation page).
    A version of this article appeared in Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2015, pp. 213-220.

  35. Dhagash Mehta, Noah S. Daleo, Florian Dorfler, and Jonathan D. Hauenstein,
    Algebraic geometrization of the Kuramoto model: equilibria and stability analysis (pdf).
    A version of this article appeared in Chaos, 25, 053103, 2015.

  36. Jonathan D. Hauenstein, Antonio Lerario, Erik Lundberg, and Dhagash Mehta,
    Experiments on the zeros of harmonic polynomials using certified counting (pdf).
    A version of this article appeared in Experimental Mathematics, 24(2), 133-141, 2015.

  37. Zachary A. Griffin and Jonathan D. Hauenstein,
    Real solutions to systems of polynomial equations and parameter continuation (pdf, computation page).
    Poster presentation by Zachary Griffin at TAGS2012 (poster).
    A version of this article appeared in Advances in Geometry, 15(2), 173-187, 2015.

  38. Jonathan D. Hauenstein, Rijun Huang, Dhagash Mehta, and Yang Zhang,
    Global structure of curves from generalized unitarity cut of three-loop diagrams (pdf).
    A version of this article appeared in Journal of High Energy Physics, 2015(2), 136, 2015.

  39. Dhagash Mehta, Jonathan D. Hauenstein, Matthew Niemerg, Nicholas J. Simm, Daniel A. Stariolo,
    Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization (pdf).
    A version of this article appeared in Physical Review E, 91, 022133, 2015.

  40. Dhagash Mehta, Tianran Chen, Jonathan D. Hauenstein, and David J. Wales,
    Newton homotopies for sampling stationary points of potential energy landscapes (pdf).
    A version of this article appeared in Journal of Chemical Physics, 141, 121104, 2014.
    JCP Editors' Choice for 2014.

  41. Dhagash Mehta, Noah S. Daleo, Jonathan D. Hauenstein, and Christopher Seaton,
    Gauge-fixing on the lattice via orbifolding (pdf).
    A version of this article appeared in Physical Review D, 90, 054504, 2014.

  42. Jonathan D. Hauenstein, Victor Pan, and Agnes Szanto,
    A note on Global Newton iteration over Archimedian and non-Archimedian fields (pdf).
    A version of this article appeared in Lecture Notes in Computer Science, 8660, 202-217, 2014.

  43. Jonathan D. Hauenstein, Jose Rodriguez, and Bernd Sturmfels,
    Maximum likelihood for matrices with rank constraints (pdf, supplementary materials).
    A version of this article appeared in Journal of Algebraic Statistics, 5(1), 18-38, 2014.

  44. Jonathan D. Hauenstein, Ian Haywood, and Alan C. Liddell, Jr.,
    An a posteriori certification algorithm for Newton homotopies (pdf).
    A version of this article appeared in Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2014, pp. 248-255.

  45. Dhagash Mehta, Jonathan D. Hauenstein, and David J. Wales,
    Certification and the potential energy landscape (pdf).
    A version of this article appeared in Journal of Chemical Physics, 140, 224114, 2014.

  46. Jonathan D. Hauenstein and Frank Sottile,
    Newton polytopes and witness sets (pdf).
    A version of this article appeared in Mathematics in Computer Science, 8(2), 235-251, 2014.

  47. Zachary A. Griffin, Jonathan D. Hauenstein, Chris Peterson, and Andrew J. Sommese,
    Numerical computation of the Hilbert function of a zero-scheme (pdf, computation page).
    A version of this article appeared in Connections Between Algebra, Combinatorics, and Geometry (S.M. Cooper and S. Saather-Wagstaff, eds.), Springer Proceedings in Mathematics & Statistics, vol. 76, Springer New York, 235-250, 2014.

  48. Daniel J. Bates, Wolfram Decker, Jonathan D. Hauenstein, Chris Peterson, Gerhard Pfister, Frank-Olaf Schreyer, Andrew J. Sommese, and Charles W. Wampler,
    Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 231, 619-633, 2014.

  49. Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, and Andrew J. Sommese,
    A bootstrapping approach for computing multiple solutions of differential equations (pdf).
    A version of this article appeared in Journal of Computational and Applied Mathematics, 258, 181-190, 2014.

  50. Jonathan D. Hauenstein, Christian Ikenmeyer, and J.M. Landsberg,
    Equations for lower bounds on border rank (pdf).
    A version of this article appeared in Experimental Mathematics, 22(4), 372-383, 2013.

  51. Jonathan D. Hauenstein, Yang-Hui He, and Dhagash Mehta,
    Numerical elimination and moduli space of vacua (pdf).
    A version of this article appeared in Journal of High Energy Physics, 2013(9), 83, 2013.

  52. Wenrui Hao, Jonathan D. Hauenstein, Chi-Wang Shu, Andrew J. Sommese, Zhiliang Xu, and Yong-Tao Zhang,
    A homotopy method based on WENO schmes for solving steady state problems of hyperbolic conservation laws (pdf).
    A version of this article appeared in Journal of Computational Physics, 250, 332-346, 2013.

  53. Dhagash Mehta, Jonathan D. Hauenstein, and David J. Wales,
    Certifying the potential energy landscape (pdf).
    A version of this article appeared in Journal of Chemical Physics, 138(17), 171101, 2013.

  54. Jonathan D. Hauenstein and Charles W. Wampler,
    Isosingular sets and deflation (pdf).
    A version of this article appeared in Foundations of Computational Mathematics, 13(3), 371-403, 2013.

  55. Daniel J. Bates, Jonathan D. Hauenstein, Timothy M. McCoy, Chris Peterson, and Andrew J. Sommese,
    Recovering exact results from inexact numerical data in algebraic geometry (pdf, computation page).
    A version of this article appeared in Experimental Mathematics, 22(1), 38-50, 2013.

  56. Jonathan D. Hauenstein and Andrew J. Sommese,
    Membership tests for images of algebraic sets by linear projections (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 219(12), 6809-6818, 2013.

  57. Jonathan D. Hauenstein,
    Numerically computing real points on algebraic sets (pdf).
    A version of this article appeared in Acta Applicandae Mathematicae, 125(1), 105-119, 2013.

  58. Gian Mario Besana, Sandra Di Rocco, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Cell decomposition of almost smooth real algebraic surfaces (pdf).
    A version of this article appeared in Numerical Algorithms, 63(4), 645-678, 2013.

  59. Jonathan D. Hauenstein and Charles W. Wampler,
    Numerically intersecting algebraic varieties via witness sets (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 219(10), 5730-5742, 2013.

  60. Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Timothy McCoy, and Andrew J. Sommese,
    Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation (pdf).
    A version of this article appeared in Journal of Computational and Applied Mathematics, 237(1), 326-334, 2013.

  61. Grigoriy Blekherman, Jonathan D. Hauenstein, John Christian Ottem, Kristian Ranestad, and Bernd Sturmfels,
    Algebraic boundaries of Hilbert's SOS cones (pdf).
    A version of this article appeared in Compositio Mathematica, 148(6), 1717-1735, 2012.

  62. Dhagash Mehta, Yang-Hui He, and Jonathan D. Hauenstein,
    Numerical algebraic geometry: a new perspective on string and gauge theories (pdf).
    A version of this article appeared in Journal of High Energy Physics, 2012(7), 18, 2012.

  63. Dhagash Mehta, Michael Kastner, and Jonathan D. Hauenstein,
    Energy landscape analysis of the two-dimensional nearest-neighbor phi^4 model (pdf).
    A version of this article appeared in Physical Review E, 85, 061103, 2012.

  64. Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Yuan Liu, Andrew J. Sommese, and Yong-Tao Zhang,
    Continuation along bifurcation branches for a tumor model with a necrotic core (pdf).
    A version of this article appeared in Journal of Scientific Computing, 53(2), 395-413, 2012.

  65. Jonathan D. Hauenstein and Frank Sottile,
    Algorithm 921: alphaCertified: Certifying solutions to polynomial systems (pdf).
    A version of this article appeared in ACM Transactions on Mathematical Software, 38(4), 28, 2012.

  66. Hafez Tari, Hai-Jun Su, and Jonathan D. Hauenstein,
    Classification and complete solution of the kinetostatics of a compliant Stewart-Gough platform (pdf).
    A version of this article appeared in Mechanism and Machine Theory, 49, 177-186, 2012.

  67. Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Yuan Liu, Andrew J. Sommese, and Yong-Tao Zhang,
    Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core (pdf).
    A version of this article appeared in Nonlinear Analysis: Real World Applications, 13(2), 694-709, 2012.

  68. Daniel J. Bates, Jonathan D. Hauenstein, and Andrew J. Sommese,
    Efficient path tracking methods (pdf).
    A version of this article appeared in Numerical Algorithms, 58(4), 451-459, 2011.

  69. Daniel J. Bates, Jonathan D. Hauenstein, and Andrew J. Sommese,
    A parallel endgame (pdf).
    A version of this article appeared in Contemporary Mathematics, 556, 25-35, 2011.

  70. Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, and Andrew J. Sommese,
    A three-dimensional steady-state tumor system (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 218(6), 2661-2669, 2011.

  71. Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Regenerative cascade homotopies for solving polynomial systems (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 218(4), 1240-1246, 2011.

  72. Charles W. Wampler, Jonathan D. Hauenstein, and Andrew J. Sommese,
    Mechanism mobility and a local dimension test (pdf).
    A version of this article appeared in Mechanism and Machine Theory, 46(9), 1193-1206, 2011.

  73. Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Yuan Liu, Andrew J. Sommese, and Yong-Tao Zhang,
    Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning (pdf).
    A version of this article appeared in Discrete and Continuous Dynamical Systems - Series S, 4(6), 1413-1428, 2011.

  74. Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Regeneration homotopies for solving systems of polynomials (pdf).
    A version of this article appeared in Mathematics of Computation, 80, 345-377, 2011.

  75. Jonathan D. Hauenstein and Andrew J. Sommese,
    Witness sets of projections (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 217(7), 3349-3354, 2010.

  76. Jonathan D. Hauenstein,
    A counter example to an ideal membership test (pdf).
    A version of this article appeared in Advances in Geometry, 10(3), 557-559, 2010.

  77. Daniel J. Bates, Jonathan D. Hauenstein, Chris Peterson, and Andrew J. Sommese,
    Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials (pdf).
    A version of this article appeared in Approximate Commutative Algebra, edited by Lorenzo Robbiano and John Abbott, a volume of Texts and Monographs in Symbolic Computation, 2010, Springer Verlag.

  78. Daniel J. Bates, Jonathan D. Hauenstein, Chris Peterson, and Andrew J. Sommese,
    A numerical local dimension test for points on the solution set of a system of polynomial equations (pdf).
    This article appeared in SIAM Journal on Numerical Analysis, 47(5), 3608-3623, 2009.

  79. Jonathan D. Hauenstein, Juan C. Migliore, Chris Peterson, and Andrew J. Sommese,
    Numerical computation of the dimensions of the cohomology of twists of ideal sheaves (pdf).
    A version of this article appeared in Contemporary Mathematics, 496, 235-242, 2009.

  80. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Stepsize control for adaptive multiprecision path tracking (pdf).
    A version of this article appeared in Contemporary Mathematics, 496, 21-31, 2009.

  81. Ashraf N. Al-Khateeb, Joseph M. Powers, Samuel Paolucci, Andrew J. Sommese, Jeffrey A. Diller, Jonathan D. Hauenstein, and Joshua D. Mengers,
    One-dimensional slow invariant manifolds for spatially homogeneous reactive systems (pdf).
    A version of this article appeared in Journal of Chemical Physics, 131(2), 024118, 2009.

  82. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Software for numerical algebraic geometry: a paradigm and progress towards its implementation (pdf).
    A version of this article appeared in Software for Algebraic Geometry, edited by M.E. Stillman, N. Takayama, and J. Verschelde, volume 148 of IMA Volumes in Mathematics and its Applications, 1-14, 2008, Springer Verlag.

  83. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Adaptive multiprecision path tracking (pdf).
    A version to this article appeared in SIAM Journal on Numerical Analysis, 46(2), 722-746, 2008.

Extended Abstracts

  1. Daniel A. Brake, Jonathan D. Hauenstein, and Alan C. Liddell, Jr.,
    Decomposing solution sets of polynomial systems using derivatives (pdf).
    A version of this extended abstract appeared in LNCS, 9725, 127-135, 2016.
    To be presented by Jonthan Hauenstien at ICMS 2016.

  2. Daniel A. Brake, Jonathan D. Hauenstein, and Andrew J. Sommese,
    Numerical local irreducible decomposition (pdf).
    A version of this extended abstract appeared in LNCS, 9582, 124-129, 2016.
    To be presented by Daniel Brake at MACIS 2015.

  3. Noah S. Daleo and Jonathan D. Hauenstein,
    Numerically testing generically reduced projective schemes for the arithmetic Gorenstein property (pdf).
    A version of this extended abstract appeared in LNCS, 9582, 137-142, 2016.
    To be presented by Jonathan Hauenstein at MACIS 2015.

  4. Daniel J. Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    On computing a cell decomposition of a real surface containing infinitely many singularities (pdf).
    A version of this extended abstract appeared in Mathematical Software - ICMS 2014, LNCS, 8592, 246-252, 2014.
    Presented by Jonathan Hauenstein at ICMS 2014.

  5. Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Bertini_real: Software for one- and two-dimensional real algebraic sets (pdf).
    A version of this extended abstract appeared in Mathematical Software - ICMS 2014, LNCS, 8592, 175-182, 2014.
    Presented by Daniel Brake at ICMS 2014.

  6. Jonathan D. Hauenstein, Nickolas Hein, and Frank Sottile,
    Certifiable numerical computations in Schubert calculus (pdf).
    Presented by Nickolas Hein at MEGA2013.

  7. Jonathan D. Hauenstein, Nickolas Hein, Christopher J. Hillar, Abraham Martin Del Campo, Frank Sottile, and Zach Teitler,
    The monotone secant conjecture in the real Schubert calculus (pdf).
    Presented by Abraham Martin Del Campo at MEGA2011 (slides).

Other Articles

  1. Jonathan D. Hauenstein and J. Michael McCarthy,
    Biologically-inspired linkage design: computing form from function (pdf).
    A version of this article appeared in SIAM News, 48(8), 2015.

Dissertation

    Jonathan D. Hauenstein,
    Regeneration, local dimension, and applications in numerical algebraic geometry (pdf),
    Ph.D. thesis, University of Notre Dame, Notre Dame, Indiana, April 2009.