Research

Current research projects:

• Dual digraphs of finite meet-distributive and modular lattices. Joint work with Miroslav Haviar and Klarise Marais. Submitted version here: arXiv pre-print
• Representable distributive quasi relation algebras. Joint work with Claudette Robinson. Submitted version here: arXiv pre-print
• A representation of odd Sugihara chains via weakening relations. Joint work with Claudette Robinson. Submitted version here: arXiv pre-print
• Compactifications of the interval topology on lattices. Joint work with Cerene Rathilal. An abstract of a recent talk can be found here: SAMS abstract

Please see the Publications tab above for papers that have already appeared in journals.

The recent work on dual digraphs of certain classes of lattices stems from a 2015 paper written with Maria Gouveia and Miroslav Haviar (see Publications).

My PhD research at Oxford was mostly related to canonical extensions for bounded lattices. The aim was to learn more about the canonical extensions of lattices which are not necessarily distributive. The theory of canonical extensions has strong links with duality theory.

Towards the end of my DPhil, I started looking at natural duality for default bilattices. This provided the starting point for joint work with Leonardo Cabrer and Hilary Priestley (see Publications) and subsequent work with Brian Davey and Miroslav Haviar.

My general research interests include:

• Relation algebras and their generalisations
• Representability for generalisations of relation algebras
• Digraphs dual to certain classes of finite lattices
• Topological duality and representation theorems for varieties of lattices
• Order topologies
• Completions of lattices and ordered sets
• Canonical extensions of bounded lattices
• Natural duality theory
• Algebraic methods in non-classical logics