Abstract
Let \({\mathcal{A}}\) be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on \({\mathcal{A}}\) parametrises an isomonodromic family of irregular connections on ℙ1 with values in the Hall algebra of \({\mathcal{A}}\). The residues of these connections are given by the holomorphic generating function for counting invariants in \({\mathcal{A}}\) constructed by D. Joyce (in Geom. Topol. 11, 667–725, 2007).
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