SR2

I'll start with the definition of a stability condition on a triangulated
category and say a bit about the space of stability conditions.
Then I'll describe some known examples of these spaces. If I have time I'll
try to explain why mirror symmetry suggests that it should be possible to equp
these spaces with interesting geometric structures.

With a theory in a logical language is associated a {\it type category}, which is a collection of topological spaces with appropriate functions between them. If the language is countable and first-order, then the spaces are compact and metrisable. If the language is a countable fragment of $L_{\omega_1,\omega}$, and so admits some formulae of infinite length, then the spaces will be Polish, but not necessarily compact.

We describe a machine for turning theories in the more expressive $L_{\omega_1,\omega}$ into first order, by using a topological compactification. We cannot hope to achieve an exact translation; what we do instead is create a new theory whose models are the models of the old theory, together with countably many extra models which are generated by the extra points in the compactification, and are very easy to describe.

We will mention one or two applications of these ideas.