Research

PRIMARY RESEARCH AREA

My primary research in mathematics investigates questions about the representation theory of Lie algebras, most recently involving bosonic and fermionic (free field) representations of twisted toroidal Lie algebras.

Lie algebra representation theory is a fascinating field with many open questions and connections to other areas of mathematics and physics, including geometry, quantum algebra, manifold theory, topology, category theory, combinatorics, vertex (operator) algebras, quantum/conformal field theory, and string theory to name a few. Connections to various areas of physics are of particular interest to me.

The historical development of the field is quite interesting as it encompasses many subfields of mathematics. It dates back to the geometric questions of Sophus Lie in the late 1800s, proceeds with the introduction of Kac-Moody algebras in the late 1960s, and continues to occupy a central role in mathematics and physics today.

If you would like any additional information about this research area or my contributions to it, please contact me!

SECONDARY RESEARCH AREAS

I am also interested in other areas including connections between mathematics, philosophy, and theology; mathematical physics; and the areas in which I have supervised undergraduate research, namely graph theory, mathematical finance, and the connections between mathematics and music.

For more on my interest in these topics, click the research statement link above or contact me.