# Introduction

I am still a Lecturer in the Mathematics Department at the University of Leeds. I teach undergraduates and taught postgraduates (see left menu) and from September will be the undergraduate admissions tutor. I am an editorial advisor for the LMS Journals and the Glasgow Maths Journal.

# Research

I am interested in aspects of abstract algebraic functional analysis, mainly Banach and operator algebras and links to abstract harmonic analysis, with some interest in Banach spaces. I am happy to supervise research students: some possible projects are listed on the Analysis website pages. Recent work with coauthors has:

• Looked at the Haagerup property for (discrete) locally compact quantum groups, and made a further study of the quantum Bohr compactification.
• Looked at what a closed subgroup of a locally compact quantum group might be.
• Showed how completely positive multipliers of operator algebraic quantum groups always arise from unitary corepresentations-- this can be seen as a non-commutative analogy of the study of positive definite functions on groups.
• Studied completely bounded but not *-preserving representations (equivalently, non-unitary corpresentations) of locally compact quantum groups.
• Constructed exotic preduals of the Banach space $\ell^1(\mathbb Z)$ which make the bilateral shift weak-star continuous, as well as initiating the classification of such preduals.