Research Plans and Proposals Andrea Schalk 's Research Plans Linear logic and category theory have given invaluable guidance in the creation of models for computation. In particular the structure on categorical models for linear logic has proved to be a useful set of requirements to ask such a model to have. The name is justified by the existence of a functor from a category of simple concrete games to ours which is well-behaved with respect to the categorical structure. Other applications include an account of how many standard models for liner logic can be seen as arising via these constructions from variants of the category of sets and relations.
Examples here are coherence spaces, phase spaces, and event structures.
This set of thoughts has a wide range of potential applications given below. Many of them are suitable for PhD theses, and I would be more than happy to answer specific questions on possible collaborations on any of them. Martin Hyland and I will continue to work jointly in this area. We suspect that our abstract constructions provide us with the right tools for identifying very simple such models. Ultimately, we would like to make the jump from giving specific such models to talking about what it takes for a category to be such a model.