Title: Variations of BPS structure and a large rank limit,
Abstract: We study a class of flat bundles, of finite rank $N$, which arise naturally
from the Donaldson-Thomas theory of a Calabi-Yau threefold $X$ via the notion
of a variation of BPS structure. We prove that in a large $N$ limit their flat
sections converge to the solutions to certain infinite dimensional
Riemann-Hilbert problems recently found by Bridgeland. In particular this
implies an expression for the positive degree, genus $0$ Gopakumar-Vafa
contribution to the Gromov-Witten partition function of $X$ in terms of
solutions to confluent hypergeometric differential equations.