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 am currently 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:

  • Studied category aspects of the theory of multipliers, and intrinsic groups, of locally compact quantum groups.
  • Supported by the EPSRC, looked at various notions of "large quantum semigroup" compactifications of locally compact quantum groups.
  • Studied the Bohr compactification for locally compact quantum groups.
  • 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.