There are three areas of research in algebra in
the Department: geometric group theory, group representation theory and semigroup theory.
Current research centres on geometric manifolds and their groups of automorphisms (particularly those carrying a hyperbolic structure); representations of lattices in Lie groups; algebraic geometry over groups.
Research in representation theory includes: projective representations of the symmetric and linear groups; the study of Yangians and Capelli identities; representations of algebraic groups, Hecke algebras and quantum general linear groups.
Research in semigroup theory is centred on covering theorems for monoids and orders in monoids.