Research

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.  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.  In representation theory, we study groups, rings, and algebras by looking at how they act on vector spaces.

I am interested in the representation theory of Lie algebras.  Lie algebras arise in many different contexts and take many forms.  Many of the questions I look at deal with Cartan-type Lie algebras, which come from considering the action of derivatives on polynomials.

As a teacher, I am also interested in how students learn mathematics. This has led me to get involved with some research in math education.   I am currently working on a project investigating the role of the textbook in undergraduate mathematics classrooms.

If you would like to learn more about any of my research, feel free to stop by to talk with me.