# 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 have a little page with some
Unpublished Work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.