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 for such varieties.
I have on-going collaborative
projects
on natural dualities, including their connections to profinite
completions and canonical extensions, 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 preprints and reprints
(with Brian Davey, Maria Gouveia and Miroslav Haviar)
Natural extensions and profinite completions of algebras
(Algebra Universalis)
(pdf)
(with Brian Davey, Maria Gouveia and Miroslav Haviar)
Multisorted dualisability: change of base
(Algebra Universalis) (pdf)
(with Brian Davey and Miroslav Haviar) Natural dualities
in partnership (Appl. Categ. Structures, 2011)
(pdf)
(with Brian Davey)
A topological approach to canonical extensions in finitely generated varieties of
lattice-based algebras (Topology and its Applications, 2011)
(pdf)
(with Brian Davey) Canonical extensions and discrete dualities for
finitely generated varieties of
lattice-based algebras (Special Issue of Studia Logica
dedicated to the memory of Leo Esakia, 2012)
(pdf)
Priestley spaces
(solicited contribution in
Lattice Theory: Foundation by George Gratzer, Subsection II.5.6)
(pdf)
Oxford, 2-3 August 2011.
List of speakers and slides of most of the talks.
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 St Anne's College and the Mathematical
Institute, Oxford, from 5-9 August, 2007. Abstracts of the 70 conference
presentations,
and slides of
almost all of these, can be found on the
conference website.