Sheffield

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.

This talk will be a tour of a couple of problems in the differential topology of

loop spaces.  We shall do a "compare and contrast" between these problems

and their finite dimensional analogues, with the aim of illustrating some of the

intriguing aspects of infinite dimensional manifolds.

The problems that we shall focus on are those of defining analogues of

differential operators on manifolds, in particular the Dirac and the

(semi-infinite) de Rham operators.