Our research covers a wide spectrum of interests from the most abstract algebra through to structures applicable to physics and biology.

Our areas of expertise cover many of the common themes of modern algebra, including: algebraic groups, representation theory, homological methods in algebra, commutative algebra, invariant theory, Lie theory, semigroup theory and universal algebra.

We collaborate with other research groups, linking our work through quantised algebraic structures (to integrable systems and mathematical physics), random walks on groups (probability), algebraic approaches to data (statistics),  and applications of invariant theory and commutative algebra to  structural and practical identifiability of mathematical models (mathematical biology).

We have a vibrant research culture, hosting many visiting researchers and PhD students from around the world. We run a regular algebra seminar series, complemented by a semigroup seminar series and an algebra study group.