Stability conditions and Stokes factors

Understand

Let A be the category of modules over a complex, finite-dimensional algebra.

• We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A.
• The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D.
• Joyce.