Chris' research is focused on the connections between combinatorics, Lie theory, knot theory, and categorical representation theory. He spends a lot of time thinking about symmetric groups, complex reflection groups and their Cherednik algebras, Kronecker coefficients, p-Kazhdan—Lusztig polynomials, and anti-spherical Hecke categories.

Ian is Professor of Mathematics and Head of School of the School of Mathematics at the University of Edinburgh. He is interested in representation theory and its applications and is a member of the Edinburgh Hodge Institute, the collective of algebraists, geometers, number theorists and topologists at the University of Edinburgh.

Radha is known for her research in the representation theory of finite groups.

 
Neil works in the field of algebra, specifically group theory and geometric representation theory. His PhD was in the theory of finite groups: the specific problem being finding the smallest degree symmetric group that an arbitrarily given finite group embeds in; and how this invariant behaves under group theoretic constructions. This is a classical problem in finite group theory having both computational and theoretical consequences.

 
In recent years, Neil’s research has focused on geometric and combinatorial aspects of representation theory. His work here has revolved around the Springer Correspondence, which provides a bijection between geometric data of an algebraic group acting on its nilpotent cone and the irreducible representations of the Weyl group of that algebraic group. Some consequences of this correspondence are that one may catalogue irreducible components of Springer fibres by means of (bi)tableaux and explicitly describe their geometry. This has applications in combinatorial representation theory and diagrammatic algebra.

Lewis is a Reader and UKRI Future Leaders Fellow at the University of Bath. His research interests include: