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."

- July 2024: Speaker at ICMS 2024 Session on Computational aspects in algebraic geometry
- August 2024: Session on "Building a Community of Support In and Out of the Classroom" at MathFest 2024
- Oct. 2024: Speaker at 2024 Fall Southeastern AMS Sectional Meeting Special Session on "Advances in applied algebraic geometry"
- June 2025: AMS Mathematics Research Community on "Real Numerical Algebraic Geometry"
- July 2025: Speaker at MCA 2025 Session on "Algebraic Geometry: the Numerical, the Random, and the Tropical"

- 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

- (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!

CV Last Updated: 06/12/2024

- 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__. - 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.__ - 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__. - 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.__. - 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__. - 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__. - 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__. - 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__. - 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.__. - 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__. - 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,

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__. - 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__. - 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__. - 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__.

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:

- PRIMUS issue on mastery based grading
- Grading for growth blog by Dr. Robert Talbert and Dr. David Clark of Grand Valley State University
- Khan academy video on mastery based learning

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

Other great resources:

- 7 study tips
- How to read a math book
- Video on how to read a math book and an example of someone following the guide
- Math writing tips by Dr. Francis Su
- Videos to help visualize mathematics content by 3Blue1Brown

__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**

- MATH 221 - Linear Algebra and Applications (Spring 2023)
__Course Syllabus__ - MATH 502 - Algebraic Structures II (Spring 2023)
__Course Syllabus__ - MATH 221 - Linear Algebra and Applications (Fall 2022)
__Course Syllabus____Course Schedule____Homework Assignments__ - MATH 353A - Ordinary and Partial Differential Equations (Pratt in Costa Rica Program -- Summer 2022 Term 2)
__Course Syllabus____Course Schedule__ - MATH 490 - Topics Course in Numerical Algebraic Geometry (Spring 2022)
__Course Syllabus__ - MATH 221 - Linear Algebra and Applications (Fall 2021)
__Course Syllabus____Homework Assignments__ - MATH 221 - Linear Algebra and Applications (Spring 2021)
__Course Syllabus____Homework Assignments__ - MATH 371 - Combinatorics (Fall 2020)
__Course Syllabus____Homework Assignments__

**University of Notre Dame**

- ACMS 20620 - Applied Linear Algebra (Fall 2019)
__Course Syllabus____Homework Assignments__

**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__)

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.

- Weiss Summer Research Scholars Summer Selection Committee Member at College of the Holy Cross
- Pi Mu Epsilon Coordinator for the Department of Mathematics and Computer Science at College of the Holy Cross
- Co-PI on Duke Faculty Advancement seed grant, themed “improving departmental climate and building community”
- Team mentor in the AWM Mentorship Program organized by the Duke Student AWM Chapter
- Member of the Duke Math Diversity, Equity, and Inclusion team

- 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)

- 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