# Barbara Bolognese (University of Sheffield): Spaces of stability conditions and degenerations

**Abstract: Spaces of stability conditions and degenerations.
Calabi-Yau categories and their spaces of stability conditions are of noticeable interest both in mathematics and in physics. By looking at some of the known example, a pattern clearly emerges and gives a fairly precise description of how they look. In particular, they all seem to have missing loci, which tend to correspond to degenerate stability conditions vanishing on spherical objects. All the naive attempts at constructing modular partial compactifications show how elusive and subtle the problem in fact is. In this talk, I will present a conjectural method to construct such partial compactifications if some additional hypoteses are satisfied, showing a fairly beautiful picture which originally comes from a Mirror-Symmetric type set up. This is joint work in progress with Tom Bridgeland and Giovanni Marchetti.**