My mathematical research is in representation theory. The idea behind representation theory is to study an algebraic object by looking at how it acts on something else (that is, some "representation" of the original object). For example, the set of transformations that leave a square unchanged form a mathematical object called a group. (One such transformation is rotation by 90° around the center of the square.) We can try to learn more about the abstract group by looking at what it does to the square.
More generally I am an algebraist, which means I like to think a lot about ideas from Linear Algebra (Math 231), Abstract Algebra (Math 303), Combinatorics (Math 421) and other ideas from Discrete Mathematics (Math 270, Math 420). I have recently started to learn about applications of discrete mathematics to biology.
As a teacher, I am also interested in how students learn mathematics. This has led me to get involved with research in math education. I am particularly interested in the role of mathematics textbooks in undergraduate classes and the ways that students use mathematics textbook.
If you would like to learn more about any of my research, feel free to stop by to talk with me. You can find a list of my publications here.