Analyticity and resurgence in wall-crossing formulas

21 May 2020 · Maxim Kontsevich, Yan Soibelman ·

We introduce the notion of analytic stability data on the Lie algebra of vector fields on a torus. We prove that the subspace of analytic stability data is open and closed in the topological space of all stability data. We formulate a general conjecture which explains how analytic stability data give rise to resurgent series. This conjecture is checked in several examples.