Our algebra and number theory research group is made up of international leaders in the field who have won between them the European Mathematical Society Prize, the Whitehead Prize of the London Mathematical Society, the Waclaw Sierpinski Prize of the Polish Academy of Sciences and the Berwick Prize of the London Mathematical Society. Our members have given invited lectures at both the International Congress of Mathematicians and the European Congress of Mathematicians. Our research centres on the following areas: non-commutative ring theory; non-commutative algebraic geometry; the geometry of algebraic numbers; Lie-theoretic representation theory; quantum algebra; category theory.