Appears in collection : Resurgence in Mathematics and Physics

In the joint paper with M. KONTSEVICH (arXiv:0811.2435) among other things we introduced the notion of stability data on graded Lie algebras, upgraded later to the notion of wall-crossing structure in arXiv:1303.3253. Both notions turned out to be suitable for spelling out wall-crossing formulas in various circumstances, in particular in Donaldson-Thomas theory of 3-dimensional Calabi-Yau categories as well as supersymmetric gauge theories in dimensions two and four. Few years ago, we wrote a paper (yet unpublished) devoted to applications of that to algebraic, analytic and resurgent properties of series arising in wall-crossing formulas. Aim of the talk is to discuss some of these ideas.