Department of Mathematics, University of Toronto
My research lies in the field of commutative algebra and 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.
Asymptotic Stabilization of Betti Diagrams of Generic Initial Systems
Stabilization of Boij-Soederberg Decompositions of Ideal Powers
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).
Mathematical Congress of the Americas, July 24-28 2017 (Montreal)