Research

My scholarly interests lie in three main areas: the intersections of commutative algebra, algebraic geometry, and graph theory; games on graphs; and scholarly teaching, including the use of mastery assessments and inquiry-based learning.

Mathematics

My dissertation research was in the exploration of the so-called containment problem. In its most general form, one may ask, given a homogeneous ideal \(I\), for which \(m\) and \(r\) is the symbolic power \(I^{(m)}\) contained in the ordinary power \(I^r\)? In addition to exploring this question in my dissertation in the context of algebraic geometry, I explored a related question in the context of edge ideals \(I(G)\). In that case, certain invariants of \(I\) related to invariants of the underlying graph \(G\).

Alongside some undergraduate students, I’ve also explored games on graphs, particularly the Game of Cycles, first described by Francis Su in his book, Mathematics for Human Flourishing.

Note to students

If you are an undergraduate and interested in research, please reach out! While it’s probably best if you’ve had at least one proof-based mathematics course (such as Dordt’s Math 212), it’s not a requirement. Let me know you’re interested, and we’ll see what we can find.

Scholarly teaching

I am also very interested in the use of research-based methods for teaching and assessment. As I describe elsewhere, I am a proponent of active learning (thought of broadly) in all my courses, and I am also interested in the use of low-stakes, mastery-based assessments tied to clear standards for the purposes of encouraging mastery of fundamental skills and the development of a growth mindset in mathematics.

Publications