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

Other interests:

  • (Marathon) swimming -- in 2023 I swam across Lake Ontario
  • 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: 06/12/2024
 
 
Download CV

Publications

  1. Timothy Duff, Viktor Korotynskiy, Tomas Pajdla, and Margaret H. Regan,
    Using monodromy to recover symmetries of polynomial systems. A version of this article will appear in Special Issue on Symbolic and Algebraic Computation: ISSAC 2023, Journal of Symbolic Computation.

  2. Margaret H. Regan,
    Using data as an input to parameterized polynomial systems.
    A version of this article appeared in Proceedings of DANGER, International Journal of Data Science in the Mathematical Sciences, World Scientific, 2(1), 63-77, 2024.

  3. 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).
    A version of this article appeared in Journal of Scientific Computing, 99(56), 2024.

  4. 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..

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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..

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

I have had the opportunity to teach a wide variety of courses at College of the Holy Cross and Duke University, with other teaching experience at the University of Notre Dame and the Westville Correctional Facility. In 2024, I was awarded the Lewis Blake Award for Excellence in Teaching from the Department of Mathematics at Duke University -- an annual postdoctoral award given for excellence in teaching. In 2020, I was awarded the Outstanding Graduate Student Teacher Award from the Kaneb Center for Teaching Excellence and The Graduate School at the University of Notre Dame. I am passionate about teaching pedagogy and I am a MAA Project NExT Fellow (Green ‘23).

 

Recently I have been exploring the use of standards based grading and active learning approaches in the classroom. Here are some resources to learn more:

Some of my sample syllabi with standards and my approach to incorporating this into a letter grade can be seen below.

Other great resources:

Current/Past Courses

College of the Holy Cross

  • MATH 135 - Calculus 1 (Spring 2024)    Course Syllabus
  • MATH 244 - Linear Algebra (Spring 2024)    Course Syllabus
  • MATH 136 - Calculus 2 (Fall 2023, Fall 2024)    Course Syllabus
  • MATH 351 - Modern Algebra 1 (Fall 2024)

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)

Service

 

Throughout my career, I have been actively committed to promoting diversity and inclusivity in mathematics through service by building community in my department, in my field, and in my broader community.






 

in my department/institution:

in my field/profession:

  • Short Communications Chair for ISSAC 2024
  • Co-Organizer: Panel on Setting a New Standard: Implementing Standards-Based Grading at the Joint Math Meetings
  • Center for Inclusive Excellence in Teaching Modeling Team Committee Member at College of the Holy Cross
  • Justice, Equity, Belonging, and Inclusion Foundations Certificate Awardee at College of the Holy Cross
  • Co-Organizer: Short Course on Polynomial Systems, Homotopy Continuation, and Applications at the Joint Math Meetings
  • Invited speaker at multiple conferences (see CV for details)

in my broader community:

  • Organizer of the Duke Math Circles Program
  • Volunteer at Expanding Your Horizons at the University of Notre Dame
  • Schmitt Leadership Conference Mentor through the University of Notre Dame