Margaret H. Regan


William W. Elliott Assistant Research Professor of Mathematics

About Me


I am currently a William W. Elliott Assistant Research Professor of Mathematics at Duke University under the mentorship of Prof. Ezra Miller. I am teaching Combinatorics this Fall 2020 and Linear Algebra and its Applications in Spring 2021. My research focuses on problems in numerical algebraic geometry and numerical analysis. Mainly, my projects involve the use of homotopy continuation to solve parametrized systems of polynomial equations with applications to computer vision and kinematics. With Ezra Miller I am exploring projects involving computing real multiparameter persistent homology.

I graduated in Aug. 2020 with 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." I was supported by the Arthur J. Schmitt Leadership Fellowship in Science and Engineering from the University of Notre Dame and a research assistantship through Prof. Jonathan Hauenstein. I was awarded the Outstanding Graduate Student Teacher Award by ND Learning | Kaneb Center for Teaching Excellence and The Graduate School at the University of Notre Dame in April 2020.

Outside of mathematics I love to read, play with my bunnies, exercise, and coach swimming. I have completed a relay crossing of the English Channel and the Mighty Mac Swim, as well as swum around Mackinac Island. These were amazing experiences in long distance swimming and scenery! I continue to train with local teams and compete in both swimming and triathlon events.

Curriculum Vitae


CV Last Updated: 10/27/2020
 

Publications


  1. 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. In preparation.

  2. Edgar A. Bernal, Jonathan D. Hauenstein, Dhagash Mehta, Margaret H. Regan, and Tingting Tang,
    Machine Learning the Discriminant Locus. Submitted (pdf).

  3. 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 will appear in LCNS, 12097, 2020.
    To be presented by Margaret H. Regan at ICMS 2020.

  4. 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 will appear in CVPR 2020.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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


Duke University - MATH 371 - Combinatorics

Course Syllabus     Homework Assignments

Exam Schedule:

  • Midterm 1 -- Wednesday, September 9 (take home)
  • Midterm 2 -- Wednesday, October 7 (take home)
  • Midterm 3 -- Wednesday, October 28 (take home)
  • Final -- Monday, November 23 from 2 - 5 pm ET
 

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)