The main research activities focus on
Commuting elements in Ore extensions. In particular exploring when commuting elements are algebraically dependent over subrings of an Ore extension. Further information at Non-commutative geometry and its applications.
Structure and representation theory for vertex operator algebras. These algebraic structures are foundational for conformal field theory and string theory in theoretical physics.Further information at Vertex operator algebras
Solving systems of polynomial equations using combinations of algebraic geometry and numerical linear algebra. This research has connections to the project Polynomial equations in geometry and computer vision.
Computational group theory, in particular investigation of maximal symmetry groups of hyperbolic space using algorithmic methods.