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Bridgeland stability conditions II

Banff International Research Station for Mathematical Innovation and Discovery

Bridgeland proved that any triangulated category has a associated space of stability conditions which is a complex manifold. In general, such spaces of Bridgeland stability conditions are difficult to compute and relatively few examples are well understood. Discrete derived categories, as defined by Vossieck, form a class of triangulated categories which are sufficiently simple to make explicit computation possible, but also non-trivial enough to manifest interesting behaviour. For these examples, combinatorial techniques can be used understand the structure and, in particular, to prove the contractibility of the corresponding space of stability conditions. I will give an overview of this topic, introducing the key definitions. Finally, I will outline an approach to producing partial compactifications of the stability spaces, by considering generalised stability conditions. This is joint work with David Pauksztello, and David Ploog and Jon Woolf.

Mathematics; Algebraic geometry; Associative rings and algebras; Representation theory

video/mp4

Author affiliation: University of Plymouth

2019-04-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69973

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/