Margaret H. Regan

Applied Math PhD Candidate

About Me

I am an Applied Math PhD Candidate (fourth year) in the Applied and Computational Mathematics and Statistics Department at the University of Notre Dame. Currently, I am a visiting researcher at the Nonlinear Algebra Semester Program at ICERM at Brown University. My advisor is Jonathan Hauenstein and I study algorithms for and applications of numerical algebraic geometry. My main interests lie in numerical algorithms dealing with overdetermined polynomial systems, parameter homotopies and homotopy conituation, and fundamental group calculations related to engineering and physics applications.

Recently, I have received an AMS Travel Award for an AMS Sectional Meeting in November of 2018, two SIAM Student Travel Awards for an algebraic geometry conference in August of 2017 and the annual meeting in July of 2018, as well as an Honorable Mention for the National Science Foundation Graduate Research Fellowship in 2016. In August of 2016, I was awarded the Schmitt Fellowship through the University of Notre Dame.

Outside of academics I love to read, play with my bunnies, exercise, and coach/teach swimming. In September of 2016 I completed a six person relay crossing of the English Channel. It was an amazing experience! Now, I train with a local masters swim team at Notre Dame and compete in both swimming and triathlons.

Curriculum Vitae

CV Last Updated: 02/05/2019


  1. 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 Regan at ICMS 2018.

  2. 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.

  3. 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.

  4. 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.



Applications of Homotopies for Overdetermined Systems


polyTop: Software for computing topology of smooth real surfaces


Numerically solving elliptic PDEs on real algebraic curves and surfaces


University of Notre Dame - ACMS 20620 - Applied Linear Algebra

Course Syllabus     Homework Assignments

Exam Schedule:

  • Midterm 1 -- Friday, March 1 (in class)
  • Midterm 2 -- Wednesday, April 17 (in class)
  • Final -- Thursday, May 9 from 4:15 - 6:15 pm

Westville Education Initiative, Holy Cross College - Math 210 - Statistics (Teaching Assistant)

Westville Education Initiative, Holy Cross College - Math 113 - College Algebra (Course Syllabus)

University of New Hampshire - Math 426 - Calculus 2 (Teaching Assistant) (student reviews)