Tuesday, January 17, 14:00

Jon Woolf (Liverpool), Stability conditions with massless objects 1, 2.

Abstract:
The space of stability conditions on a triangulated category can be partially compactified by adding points corresponding to `lax stability conditions' which are allowed to have massless objects. The massless objects of a lax stability condition form a thick subcategory and there is a second, related, partial compactification obtained by adding points corresponding to stability conditions on the respective quotient categories.
These partial compactifications have a surprisingly simple local structure: the massive and massless parts of the stability condition `de-couple' leading to a local product form. The key technical ingredient is a new result for constructing slicings on a triangulated category from ones on a thick subcategory and the respective quotient.
I will illustrate the partial compactifications in some simple cases, and also point out an intriguing connection between its `real skeleton' and the g-fans of algebraic hearts.
This is all joint work with Nathan Broomhead, David Pauksztello and David Ploog.