Department of Mathematics, University of Toronto
I approach all of my work as a scholar, and my approach to working is guided by what I learned as a mathematician: keep asking questions and follow interesting pathways where they lead. I have one foot in the Math Research world, where I am a commutative algebraist, and one foot in the math education sphere, where my work would be classified as the Scholarship of Teaching and Learning.
My math research works to understand infinite collections of polynomials. More specifically, I am interested in understanding the asymptotic behaviour of graded systems of polynomial ideals, such as the system given by taking powers of a fixed ideal. Currently I am studying relationships between the graded Betti numbers of different ideals within a single graded system.
Powers of graphs & applications to resolutions of powers of monomial ideals (with Susan M. Cooper, Sabine El Khoury, Sara Faridi, Susan Morey, Liana M. Sega, Sandra Spiroff), Research in the Mathematical Sciences, to appear (2022).
Morse resolutions of powers of square-free monomial ideals of projective dimension one. With Susan M. Cooper, Sabine El Khoury, Sara Faridi, Susan Morey, Liana M. Sega, Sandra Spiroff. Journal of Algebraic Combinatorics, to appear.
Simplicial resolutions for the second power of square-free monomial ideals (with Susan Cooper, Sabine El Khoury, Sara Faridi, Susan Morey, Liana M. Sega and Sandra Spiroff). Women in Commutative Algebra -- Proceedings of the 2019 WICA Conference AWM Series. (Claudia Miller, Janet Striuli, Emily E. Witt). Springer, 2022. Pages 193--205.
Asymptotic Stabilization of Betti Diagrams of Generic Initial Systems
Stabilization of Boij-Soederberg Decompositions of Ideal Powers, Journal of Pure and Applied Algebra , 223.2 , 571-579 (2019).
The Symbolic Generic Initial System of Almost Linear Point Configurations in P2 , Rocky Mountain Journal of Mathematics, 46(1), 283-299 (2016).
Non-simplicial decompositions of Betti diagrams of complete intersections (with Courtney Gibbons, Jack Jeffries, Claudiu Raicu, Branden Stone, and Bryan White), Journal of Commutative Algebra, 7(2), 189–206 (2015).
The Generic Initial Ideals of Powers of a 2-Complete Intersection, Journal of Commutative Algebra, 7(1), 55–75 (2015).
The Asymptotic Behaviour of Symbolic Generic Initial Systems of Generic Points, Journal of Pure and Applied Algebra, 218, 381–390 (2014).
The Limiting Shape of the Generic Initial System of a Complete Intersection, Communications in Algebra, 42, 2299–2310 (2014).
Much of my scholarly work is centred around the Scholarship of Teaching and Learning. Some current projects include:
Sharing Our Stories to Build Community, Highlight Bias, and Address Challenges to Authority, Picture a Professor: Intersectional Teaching Strategies for Interrupting Bias about Faculty and Increasing Student Learning, edited by Jessamyn Neuhaus. West Virginia University Press, 2022.
Telling Women's Stories: A Resource for College Mathematics Instructors, Journal of Humanistic Mathematics 9(2) (2019)
Designing Opportunities for Mathematical Creativity: Modifying an existing course , to appear in PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 30(3) (2020)
Using our Classroom Walls: A Project for Visualizing the Development of Conceptual Understanding , PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 28(3), 223–235 (2018).
Designing Creative Courses with Students in Mind, ARES Seminar (Fall 2021)
Teaching on Empty: Trauma, Achievement, and What's Next in Our Mathematical Community, CMESG (Summer 2021)
Building Understanding by Understanding our Students: Techniques for Teaching Teams, STHLE (Summer 2021)
Listening before Teaching: Building Mathematical Understanding by Understanding Our Students, Invited Plenary, CMS (Winter 2019)
Welcome to Our New Classroom: MY150, University of Toronto Teaching & Learning Symposium (Spring 2019) -Worksheet
Active Learning: Engaging International Students, University of Waterloo Teaching & Learning Symposium (Spring 2019)
A first-year seminar on mathematical creativity, Mathematical Themes of a First-Year Seminar, MAA MathFest (Summer 2018)
Using women's stories in a first-year mathematics seminar, Impact of Women on Research and Education in Mathematics, BIRS (Spring 2018)