Topological recursion and uncoupled BPS structures for hypergeometric spectral curves

The notion of BPS structure formalizes many of the structures appearing in the study of four-dimensional N=2 QFTs by Gaiotto-Moore-Neitzke as well as Bridgeland's spaces of stability conditions and the generalized Donaldson-Thomas (equivalently, BPS) invariants. We outline a correspondence which relates the BPS invariants, central charges, and solutions to certain Riemann-Hilbert problems with the topological recursion free energies and Voros symbols of corresponding quantum curves, which we have shown for the special case of spectral curves of "hypergeometric type". This is joint work with K. Iwaki, arXiv:2010.05596+ ongoing.