Lattice theory, ordered sets, ordered topological structures, and
related areas; applications in logic and computer science.
Specifically, my work has involved
Priestley duality for distributive lattices, topological dualities
for varieties of distributive lattices with additional operations
and the theory of natural dualities.
I have on-going collaborative
on natural dualities, including their connections to other constructions, with
In recent years I have been working, in collaboration with
on duality and canonical extensions.
In particular, we are preparing a research monograph,
Lattices in Logic, for Oxford University Press.
Recent publications and preprints
(with M.J. Gouveia) Profinite completions and canonical extensions of semilattice reducts of
distributive lattices (Houston J. Math. 39
(with A.P.K. Craig and M. Haviar) A fresh perspective on canonical extensions for bounded lattices
(Appl. Categ. Structures
(with M.J. Gouveia) Canonical extensions and profinite completions
of semilattices and lattices (Order 31
GAIA 2013 (conference in honour of Brian Davey, Melbourne, July 2013): slides [pdf]
BLAST 2013 (Chapman University, California, August 2013): slides I
[pdf]; slides II [pdf]
George Boole Mathematical Sciences Conference, Theme 2: From Boole's Algebra of Logic to Boolean Algebra, and Beyond (University College Cork, August 2015): slides
Research Workshops on Duality Theory in Algebra, Logic and
Computer Science, Oxford, 13-14 June and 15-17 August, 2012.
Sponsored by EPSRC and the British Logic Colloquium.
Workshop on Duality Theory, Oxford, 2-3 August 2011
Conference TANCL'07 (Algebraic and Topological Methods in Non-classical
This conference, sponsored by the London Mathematical Society and the British Logic
Colloquium, was held at the Mathematical
Institute, Oxford, 5-9 August, 2007. It was the third in the biennial series now using the acronym TACL
(Topology, Algebra and Categories ib Logic)