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  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.