I am currently Professor of Pure Mathematics in the Pure Mathematics Research Centre at Queen's University Belfast.

I studied for a PhD at Chelsea College, London under the supervision of Francis Jellett working initially on the theory of compact convex sets but completing a thesis with the title of Linear operators between partially ordered Banach spaces and some related topics. Shortly after that, I switched direction to work on vector lattices and decided to draw a line under my study of compact convex sets by writing up a set of notes on Affine functions on compact convex sets.

My current research is into Banach lattices and linear operators on them. In recent years I have increasingly concentrated on the order structure of spaces of linear operators between two Banach lattices and the relationship between various spaces. Typical questions I have investigated are when the space of regular operators (i.e. those which are the difference of two positive operators) is a lattice or when it coincides with the space of all bounded operators. A further strand concerns domination properties which ask when a positive operator must inherit some desirable property which is possessed by a positive operator which dominates it.

A list of those of my publications that have reached MathSciNet may be found here, whilst this list contains some more recent publications as well as items like book reviews, articles on computing and mathematics teaching plus some papers in theoretical physics where I have contributed my (rather minor!) computing skills.

Below are either slides or the text for various talks that I have given over the years which may still be of some interest to people either for expository reasons or because they contain results or problems that have not been published elsewhere.

In March 2008, I was to talk at a workshop in Sevilla, but was prevented by illness. I was to give a series of talks on The order structure of regular operators between Banach lattices. This contains some material that is not yet published elsewhere so may be of interest.

At the workshop preceding the Positivity V conference which was held here in July 2007, I gave two series of expository talks. One was on Vector and Banach Lattices and the other on Operators on Banach Lattices.

In the UK there is a long standing tradition that newly appointed or promoted professors must give a public lecture entitled an inaugural lecture. The audience for this is likely to include not only academic staff from a wide variety of disciplines but also friends and relatives. I gave mine in 1994 and it was the closest that I have ever come to preparing a popular talk. The text (but not the accompanying graphics) is at Pure Mathematics? Positively Applied! I have to admit that afterwards my father confessed that the lecture was the most boring hour of his life!

In 1994 I gave a series of lectures at the Middle East Technical University in Ankara. For a theme I assembled some material, that was familiar, in a novel way by concentrating on Operator Theoretic Characterizations of Completeness in Riesz Spaces.

I think that the very first talk that I gave at a major conference was at Silivri in Turkey in 1976. I prepared far too much material but did at least prepare handouts. This assembles results on the Structure Space and Ideal Centre of a Banach Lattice in a way that I have not seen elsewhere and includes some results (unfortunately only the statements) that have never been published.

In April 2011 I visited Chengdu and Xi'an in China and took many photographs during the visit. I gave several lectures in Chengdu as well as visiting the Wuhou Memorial Temple, followed by Jinli Street, a tourist shopping area; the Water Conservancy Project at Duijangyan as well as lunch afterwards; the Jinsha site museum and the Giant Panda Breeding Centre where I saw not only Giant Pandas but also Red Pandas, which are more closely related to the fox than the giant panda. These photographs show some of the many people who looked after us in Chengdu. I then visited Xi'an where after lecturing I visited the Terracotta Army; the Huaqing Hot Springs which was the location of Chiang Kai-shek's headquarters at the time of the Xi'an incident in 1936; the Big Grey Goose Pagoda; the Forest of Stone Steles museum; climbed the Xi'an Bell Tower and looked at the city views from there and climbed the Xi'an City Walls. On the final night in Xi'an we had a great meal. Finally, here are some photographs of interesting restaurant scenes, some of primary school children practising for their May Day display and some street scenes, including a lattice shop!