Over the past 15 years, I have taught calc I-III, differential equations, survey of calculus (light calculus course at UArk), discrete math, group theory, ring theory, linear algebra with differential equations (JMU), intro and intermediate linear algebra, intro to commutative algebra (at the grad level), intro to stats, and mathematics in our society. I taught a GRE prep course for the quantitative reasoning portion of the exam the summer after I graduated college, and last spring I got a TA position for Erdös Institute's data science boot camp.

You can see some of my old teaching webpages and materials by going to the ArkansasWebsite folder in my GitHub repository, AcademiaMaterials. Unfortunately my more recent online materials are on Canvas (JMU) and Moodle (MHC and Centre).

It turns out that I can still access my MHC materials on Moodle! Here are some slides I used to teach calc II remotely during SY 2020-2021. It took me about a month to make them, but I taught the course four times in a row with those slides (MHC switched to a module system during the pandemic) and by the fourth time they, and the other course materials, were well-polished. Here are a few more materials: the syllabus, the technology guide, and the course calendar, all made using $\LaTeX$.

My Georgia Tech website still exists, too (as of May 2024), but the videos I recorded of my lectures during COVID are no longer available (Georgia Tech sunset BlueJeans, the platform I used to record the lectures, in favor of Zoom).

My research area is in commutative algebra, the study of solutions to polynomial systems of equations. Commutative algebra can be thought of as a generalization to linear algebra, the study of solutions to linear systems of equations. A system of equations is linear means the variables appear with numerical coefficients only, they don't have powers on them, they are not multiplied together, and they are not part of a function (e.g., $\sin(x)$). For example:

In polynomial systems of equations, the variables can have integer exponents on them, and they can be multiplied together. Here is a system of polynomial equations in three variables: While linear systems can easily be solved by computers using matrices, polynomial systems have no such analog. Instead, we study ideals, or collections of sums of polynomial multiples of the left-hand sides (after moving everything to the left to get a $0$ on the right) of the equations in the system.

My main vein of research since getting my Ph. D. has been my thesis topic, ideals generated by principal minors. These ideals have applications in algebraic statistics, most notably the PMAP problem, and not much is known about them. In summer of 2022 I mentored 3 students in the Georgia Tech REU (an NSF-funded program called Research Experience for Undergraduates) on a project exploring the toric structure of the ideals generated by principal $2$-minors, which in addition, have applications in integer programming. I gave this talk at the Joint Math Meetings (JMM) in January 2023.

All of my papers, published or not, are available at arxiv.org. I have given several talks on most of those projects (see my CV). Here is one of the later, more polished versions of the Bertini theorem talk that I also gave at JMM 2023, while here is the earliest version of the matroid varieties talk I gave, which was at the colloquium at MHC and aimed toward undergrads. For the local cohomology project, I gave this version of the talk at both JMM and KUMUNUjr (now known as URiCA) in 2017. Finally, I gave this talk at JMM 2014 on the two papers that resulted from my thesis. It is also the earliest version of that talk, and I spent a lot of time learning and using TikZ to make the slides stand out.