# Margaret H. Regan

William W. Elliott Assistant Research Professor of Mathematics

William W. Elliott Assistant Research Professor of Mathematics

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.

Conference sessions organized:

- AMS Special Session on Multiparameter persistence in theory and practice, AMS Southeastern Sectional Meeting, University of Virginia, March 2022 (with Ezra Miller, Duke University and Havard Bjerkevik, TU Graz).
- Minisymposium on New trends in polynomial system solving, (Virtual) SIAM Conference on Applied Algebraic Geometry, Texas A&M University, Aug. 2021 (with Simon Telen, MPI MiS Leipzig).

CV Last Updated: 05/25/2022

- Mirja Rotzoll, Margaret H. Regan, and M. John D. Hayes,

Kinematic geometry of spatial RSSR mechanisms.*In progress*. - Woojin Kim, Ezra Miller, Samantha Moore, and Margaret H. Regan,

Functorial endpoints for multiparameter persistence.*In progress*. - Shreya Arya, William He, Ezra Miller, and Margaret H. Regan,

Computing presentations for real biparameter persistent homology from fly wing vein splines.*In progress*. - 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*. - Timothy Duff, Viktor Korotynskiy, Tomas Pajdla, and Margaret H. Regan,

Galois/monodromy groups for decomposing minimal problems in 3D reconstruction.*Submitted*(__pdf__). - Edgar A. Bernal, Jonathan D. Hauenstein, Dhagash Mehta, Margaret H. Regan, and Tingting Tang,

Machine Learning the Discriminant Locus.*Submitted*(__pdf__). - 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__. - 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__. - 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__. - 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__. - 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__. - 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__. - 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__.

Duke University - MATH 221 - Linear Algebra and Applications (Fall 2022)

__Course Syllabus__ __Course Schedule__ __Homework Assignments__

*Exam Schedule:*

- Midterm 1 -- Tuesday, September 27 (in class)
- Midterm 2 -- Tuesday, October 25 (in class)
- Midterm 3 -- Tuesday, November 29 (in class)
- Final -- either Saturday, December 17 from 7 - 10 pm ET (Section 1) or Thursday, December 15 from 2 - 5 pm ET (Section 2)

Duke University Pratt in Costa Rica Program - MATH 353A - Ordinary and Partial Differential Equations (Summer 2022 Term 2)

__Course Syllabus__ __Course Schedule__

*Exam Schedule:*

- Midterm -- Thursday, July 21 (in class)
- Final -- Saturday, August 6

Duke University - MATH 490 - Topics Course in Numerical Algebraic Geometry (Spring 2022)

*Exam Schedule:*

- Midterm 1 -- Thursday, February 17 (in class)
- Midterm 2 -- Thursday, March 17 (in class)
- Final presentations -- Friday, April 29 from 7 - 10 pm ET

Duke University - MATH 221 - Linear Algebra and Applications (Fall 2021)

__Course Syllabus__ __Homework Assignments__

*Exam Schedule:*

- Midterm 1 -- Tuesday, September 21 (in class)
- Midterm 2 -- Tuesday, October 19 (in class)
- Midterm 3 -- Thursday, November 18 (in class)
- Final -- either Friday, December 10 from 9 am - 12 pm ET (Section 1) or Saturday, December 11 from 7 - 10 pm ET (Section 5)

Duke University - MATH 221 - Linear Algebra and Applications (Spring 2021)

__Course Syllabus__ __Homework Assignments__

*Exam Schedule:*

- Midterm 1 -- Wednesday, February 17 (in class)
- Midterm 2 -- Wednesday, March 17 (in class)
- Midterm 3 -- Wednesday, April 14 (in class)
- Final -- Wednesday, April 28 either from 9 am - 12 pm ET (Section 1) or 2 - 5 pm ET (Section 2)

Duke University - MATH 371 - Combinatorics (Fall 2020)

__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 (Fall 2019)

__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__)