Mathematics

Research Interests

My research is in a field known as 'higher-dimensional algebra'. My dissertation, Lie 2-Algebras, was written under the guidance of John Baez. My work blends Lie theory with elements of category theory and has connections to braid theory and Lie algebra cohomology. I am also interested in the relationship between Lie algebras and algebraic structures known as quandles. Thus, my interests lie in quantum algebra and quantum and geometric topology.

My current interests, supported by the Collaboration Grants for Mathematicians program through the Simons Foundation (2015 - 2020), focus on self-distributive structures such as quandles and racks. A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of group conjugation and algebraically encode the Reidemeister moves from classical knot theory. I am interested in the relationships between self-distributive structures and their (co)homology and crossed modules, group and Lie algebra (co)homology theories, and knot and knotted surface invariants.

Recent Publications

(for a complete list, please see my Curriculum Vitae)

Recent Grants

(for a complete list, please see my Curriculum Vitae)

Recent Presentations

(for a complete list, please see my Curriculum Vitae)

Fun Stuff