The main research activities focus on
Structure and representation theory for vertex operator algebras. These algebraic structures are foundational for conformal field theory and string theory in theoretical physics.
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.
Classifying spaces of compact Lie groups. This involves p-compact groups and fusion systems but also group cohomology and representation theory. The work often involves the use of computer algebra.
Algorithms for constructing canonical bases of ideals (Gröbner bases) and subalgebras (SAGBI bases) and the usage of such bases to solve geometric and algebraic problems.