What's my research all about?

I study representation theory, which is an area of mathematics which uses linear algebra to study problems arising from abstract algebra. 

I like to describe my research using the following metaphor: If a space explorer were to encounter an alien species on a different planet, they might hide behind a rock and study the alien's behavior. Or, if they are feeling particularly bold, they might toss a banana to the creature and see how it responds to the banana. The point is, there is much to be learned by studying how something can interact with its surroundings.

Representation theorists are explorers on the mathematical frontier of Abstract Algebra. The algebraic creatures I study arise in the mathematical study of symmetry, and the have strange names like "the symmetric group" and "the type Q Lie superalgebra." When I encounter one of these mathematical beasties, I study how it can interact with other mathematical objects, like "vector spaces."  These sorts of interactions can be encoded using "representations" and a lot of interesting mathematics arises from studying these things.

The subject has lots of applications to other fields where symmetry is important: In math, that includes topology, knot theory, and number theory. Outside of math, this includes physics, chemistry, and computer science.

Myself, with collaborators Jieru Zhu, Jon Kujawa, and Rob Muth