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
projects
on natural dualities, including their connections to other constructions, with
In recent years I have been working, in collaboration with
Mai Gehrke,
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
(2013),
1117-1136)
[pdf]
(with A.P.K. Craig and M. Haviar) A fresh perspective on canonical extensions for bounded lattices
(Appl. Categ. Structures
21
(2013), 725-749)
[arkiv]
(with M.J. Gouveia) Canonical extensions and profinite completions
of semilattices and lattices (Order 31
(2014),
189-216)
[pdf]
(with L.M. Cabrer) Distributive bilattices from the perspective of natural duality theory
(Algebra Universalis,
(2015),
103-141)
[arXiv]
(with L.M. Cabrer and A.P.K. Craig) Product representation for default bilattices: an application of natural duality theory (J. Pure Appl. Algebra 219
(2015),
2962-2988) [arkiv]
(with L.M. Cabrer) Gödel algebras: interactive dualities and their applications (Algebra Universalis
(a volume dedicated to Brian Davey for his 65th birthday)
74 (2015), 87-116)
[arkiv]
(with B.A.
Davey and M. Haviar) Piggyback dualities revisited (to appear in Algebra Universalis)
[arkiv]
(with L.M. Cabrer) A general framework for product representations: bilattices and beyond (to appear in
Log. J. IGPL) [arkiv]
(with B.A.
Davey and M. Haviar) Bohr compactifications of algebras and structures
(submitted) [arkiv]
(with L.M. Cabrer) Natural dualities through
product representations: bilattices and beyond
(submitted) [arkiv]
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
[pdf]
Events organised
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
Logics III)
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)