Research

Current interests

Mathematical Logic: Proof theory of Linear Logic, Intuitionistic Logic and Classical Logic. Categorical Semantics of Proofs, Full Completeness Theorems; Models for Linear Logic, Game Semantics for Proofs, Geometry of Interaction, Abstract Interpretations.
Category Theory: Categorical algebra, Higher Dimensional Categories, Generalised Operads, Higher Dimensional Algebra, Topological Field Theories, Reconstruction Theorems, Cobordism Categories, Vertex Algebras.
Theoretical Computer Science: Realizability Models, Synthetic Domain Theory,
Polymorphism, Linear Types Systems, Game Semantics for Computation, Abstract Games.

Other areas of expertise

The Pure Lambda Calculus; Higher Type Recursion Theory; Sheaf and Topos Models for Intuitionism; Topos Theory and Locale Theory.

Research material

Publications

I am making as much of my published work available as I can. I have put together a collection of Pre-millenium Papers, that is, papers covering the year 1976-2000. I am also trying to maintain a collection of Post-millenium Papers, papers from 2001 onwards.

In addition I intend to keep annotated records of publications by decade. Some of this is more complete beginning of April 2016.
Publications 1971-80
Publications 1981-90
Publications 1991-00

Miscellaneous Resources

I aim to have a page with Unpublished Work and other miscellaneous material.
I have a fairly random selection of slides. In the case of talks given in the last few years I am able to give confident dates and venues. In some older cases the slides have been retrieved from filing cabinets and I cannot place them with any certainty. I am happy to hear from anyone who can. Also if anyone can retrieve the slides which I left in Edinburgh after a series of talks on (I think) Abstract Games then I would be grateful to have them. They might have more than historical interest.


Research Projects

Summary of recent EPSRC project Uniform Game semantics etc made available as required.