Abstract:

A stability condition on a triangulated category turns the category into a geometric object. We can then import powerful techniques from geometry to the study of triangulated categories and stability manifolds. I will elaborate on this theme. Specifically, I will describe how a stability condition defines a metric on the category. I will describe how this metric can be used to construct a compactification of the stability manifold, using ideas inspired by the study of metrics on Riemann surfaces, namely Teichmuller theory. I will then discuss potential applications, examples, and unexplored areas.

*This is part of a series of talks, full program can be found here.