Scholarly interests

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


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 (simple) graph $G$.

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.

I compiled some WeBWorK-based preview activities for an elementary linear algebra course.