Sarah Mayes-Tang

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.

Mathematics Research

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.

Math Research Publications

• 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).

Scholarship of Teaching and Learning