Abstract:

This talk loosely follows from Tony's talk a few weeks ago, but I will recall all necessary definitions. Given a category, the auto-equivalence group acts on it and on related natural objects. If the category is triangulated, it is nice to consider the induced action on the Bridgeland stability manifold, which is a manifold naturally associated to the category.

It is usually not easy to compute the stability manifold of a given category. But based on the small amount of empirical evidence, one might wonder whether these manifolds are always contractible. I will discuss a conjectural approach to tackle this question in a particular rich class of examples. The simplest concrete example (which we have worked out to a great extent) will lead us to point configurations in the plane and some peculiar combinatorics. This is joint work with Anand and Tony.