The interests of the group cover a wide range of topics in pure mathematics, having recently expanded in noncommutative algebra, algebraic geometry and geometric group theory.

Many high quality appointments have been made in recent years and the group has won many prominent national and international awards and fellowships. There are common interests with other groups, particularly Mathematical Physics. Our research now spans:

- Algebra and Representation Theory: algebraic combinatorics, geometric group theory, Lie theoretic representation theory, noncommutative algebra, noncommutative geometry, representations of quivers, semigroup theory.
- Algebraic Geometry: birational algebraic geometry, derived categories and their applications, moduli spaces, derived algebraic geometry, singularity theory, toric geometry.
- We have strong and well-developed interests in higher dimensional algebraic topology, category theory and its applications, and the geometry of algebraic numbers.