The Department of Pure Mathematics is one of the leading centres for Pure Mathematics research in the UK, with a well established international reputation for quality in research and teaching. The Department has 23 academic staff, several research fellows and 30 research students. Postgraduate research areas are listed below and offer supervision in associative algebras and rings; representation theory of algebras and quivers, and connections with Lie theory, algebraic geometry and singularities; infinite groups; permutation groups; Banach algebras; operator algebras; harmonic analysis; applications of functional analysis to control theory; differential geometry, and its application to soliton dynamics; singularity theory; generalised recursive theory; model theory; set theory; proof theory. The Department runs regular seminars and annual graduate courses in the main research areas listed below, as well as more general pure mathematics colloquia.