About USMC 07

Certain properties of mathematical objects are peculiar to particular models. For instance, not every group is simple, not every manifold is differentiable and not every field is algebraically closed. Determining which results hold purely in virtue of a particular structure carried by an object allows one to transfer a result from one area to another. Systematising this process has led, on the one hand, to universal algebra and the study of varieties and quasivarieties of algebras and, on the other hand, to category theory and the study of monads, functorial theories and their higher dimensional counterparts. In addition, the realisation that various logics are essentially equivalent to theories of varieties of algebras has allowed algebra and logic to enrich each other in often unexpected ways. More recently, all three fields have found fruitful applications in computer science, in such areas as type theory, denotational semantics and concurrency theory.

Unfortunately, communication between universal algebraists, category theorists and logicians has been all too uncommon. Some happy counterexamples to this situation do exist. For instance, universal algebraists' characterisation of free lattices led to category theorists' characterisation of free bicompletions of categories, which in turn led to logicians showing that these provide the natural semantic setting for additive linear logic. Computer scientists have subsequently used this to provide a natural environment for the semantics of message passing protocols.

The main aim of this workshop is to foster communication between researchers working in these fields in the hope that it will lead to fruitful new interdisciplinary collaborations and, of course, beautiful new theorems. The event also aims to benefit PhD students doing research in these fields, by providing a venue for them to present their on-going works and to get feedbacks from the experts in the fields.