Margaret H. Regan

I am currently an Assistant Professor at the College of the Holy Cross in the Department of Mathematics and Computer Science. Previously, I was a William W. Elliott Assistant Research Professor of Mathematics at Duke University under the mentorship of Prof. Ezra Miller, where I was awarded the Lewis Blake Award for Excellence in Teaching. In 2020 I received a PhD in Applied and Computational Mathematics and Statistics advised by Prof. Jonathan Hauenstein at the University of Notre Dame. The title of my dissertation is "Parameterized polynomial systems and their applications."

Current/upcoming activities:

Research interests:

  • Numerical (real) algebraic geometry and numerical analysis
  • Algorithms for solving parameterized polynomial systems and analyzing solution behavior
  • Applications of all of the above - e.g., computer vision, kinematics, biology, and more
  • Commutative algebra and real multi-parameter persistent homology

Other interests:

  • (Marathon) swimming
  • Triathlons
  • Reading fantasy and sci-fi books
  • True crime podcasts
  • Knitting and needlepoint
  • Animals - my 2 dogs (Hutch and Steuben) and my 2 rabbits (Flopsy and Lucky) especially!

Curriculum Vitae

CV Last Updated: 12/19/2023
 
 
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Publications

  1. Timothy Duff, Viktor Korotynskiy, Tomas Pajdla, and Margaret H. Regan,
    Using monodromy to recover symmetries of polynomial systems. Submitted.

  2. Wenrui Hao, Jonathan D. Hauenstein, Margaret H. Regan, and Tingting Tang,
    A numerical method for solving elliptic equations on real closed algebraic curves and surfaces (pdf). Submitted.

  3. Timothy Duff, Viktor Korotynskiy, Tomas Pajdla, and Margaret H. Regan,
    Using monodromy to recover symmetries of polynomial systems (pdf).
    A version of this article appeared in ISSAC 2023, Association for Computing Machinery, 251-259..

  4. Mirja Rotzoll, Margaret H. Regan, Manfred L. Husty, and M. John D. Hayes,
    Kinematic geometry of spatial RSSR mechanisms (pdf).
    A version of this article appeared in Mechanism and Machine Theory, 185, 105335, 2023.

  5. Edgar A. Bernal, Jonathan D. Hauenstein, Dhagash Mehta, Margaret H. Regan, and Tingting Tang,
    Machine Learning the Discriminant Locus (pdf).
    A version of this article appeared in Journal of Symbolic Computation, 115, 409-426, 2023.

  6. Timothy Duff and Margaret H. Regan,
    Polynomial systems, homotopy continuation, and applications (pdf).
    A version of this article appeared in Notices of the American Mathematical Society, 70(1), 151-155, 2023.

  7. Ricardo Fabbri, Timothy Duff, Hongyi Fan, Margaret H. Regan, David da Costa de Pinho, Elias Tsigaridas, Charles W. Wampler, Jonathan D. Hauenstein, Peter Giblin, Benjamin Kimia, Anton Leykin, and Tomas Pajdla,
    TRPLP - Trifocal relative pose from lines at points (pdf).
    A version of this article appeared in IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 1-14, 2022.

  8. Timothy Duff, Viktor Korotynskiy, Tomas Pajdla, and Margaret H. Regan,
    Galois/monodromy groups for decomposing minimal problems in 3D reconstruction (pdf).
    A version of this article appeared in SIAM Journal on Applied Algebraic Geometry, 6(4), 740-772, 2022..

  9. Jonathan D. Hauenstein and Margaret H. Regan,
    Real monodromy action (pdf).
    A version of this article appeared in Applied Mathematics and Computation, 373, 124983, 2020.

  10. Ricardo Fabbri, Timothy Duff, Hongyi Fan, Margaret H. Regan, David da Costa de Pinho, Elias Tsigaridas, Charles W. Wampler, Jonathan D. Hauenstein, Peter Giblin, Benjamin Kimia, Anton Leykin, and Tomas Pajdla,
    TRPLP - Trifocal relative pose from lines at points (pdf).
    A version of this article appeared in 2020 IEEE/CVPR Conference on Computer Vision and Pattern Recognition.

  11. Jonathan D. Hauenstein and Margaret H. Regan,
    Evaluating and differentiating a polynomial using a pseudo-witness set (pdf, computation page).
    A version of this article appeared in LCNS, 12097, 61-69, 2020.
    Presented by Margaret H. Regan at ICMS 2020.

  12. Jonathan D. Hauenstein and Margaret H. Regan,
    Adaptive strategies for solving parametrized systems using homotopy continuation (pdf, computation page).
    A version of this article appeared in Applied Mathematics and Computation, 332, 19-34, 2018.

  13. Danielle A. Brake, Jonathan D. Hauenstein, and Margaret H. Regan,
    polyTop: Software for computing topology of smooth real surfaces (pdf, software).
    A version of this extended abstract appeared in LNCS, 10931, 397-404, 2018.
    Presented by Margaret H. Regan at ICMS 2018.

  14. Peter J. Collings, Joshua N. Goldstein, Elizabeth J. Hamilton, Bejamin R. Mercado, Kenneth J. Nieser, and Margaret H. Regan,
    The nature of the assembly process in chromonic liquid crystals .
    A version of this article appeared in Liquid Crystals Reviews, 3(1), 1-27, 2015.

  15. Elizabeth A. Mills, Margaret H. Regan, Vesna Stanic, and Peter J. Collings,
    Large Assembly Formation via a Two-Step Process in a Chromonic Liquid Crystal .
    A version of this article appeared in The Journal of Physical Chemistry B, 116 (45), 13506-13515, 2012.

Research

CompVis

Applications of Homotopies for Overdetermined Systems

polyTop

polyTop: Software for computing topology of smooth real surfaces

ellipticPDEs

Numerically solving elliptic PDEs on real algebraic curves and surfaces

realMonodromy

Real monodromy action

Teaching

College of the Holy Cross

  • MATH 135 - Calculus 1 (Spring 2024)
  • MATH 244 - Linear Algebra (Spring 2024)
  • MATH 136 - Calculus 2 (Fall 2023)    Course Syllabus

Duke University

University of Notre Dame 

Westville Education Initiative, Holy Cross College

  • MATH 210 - Statistics (Teaching Assistant -- Fall 2017)
  • MATH 113 - College Algebra (Summer 2017)     Course Syllabus

University of New Hampshire 

  • MATH 426 - Calculus 2 (Teaching Assistant -- Spring 2015) (student reviews)