Title: The space of augmented stability conditions

Abstract: I will survey recent joint work with Daniel Halpern-Leistner which constructs a partial compactification of (a quotient of) the space of Bridgeland stability conditions on a triangulated category. The partial compactification is modular in the sense that its boundary points parameterise a new type of homological structure: an augmented stability condition. I will introduce augmented stability conditions and explain some of the key properties of the space parameterising them. I will also explain how certain boundary strata of this space relate to braid group actions on semiorthogonal decompositions.