# 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.