Stable pairs, flat connections and Gopakumar–Vafa invariants

We offer a quick introduction to certain recent aspects of Donaldson–Thomas theory in the context of curve-counting invariants. We present a new computation which recasts the correspondence between the Gromov–Witten and Donaldson–Thomas theories of a Calabi–Yau threefold in the language of flat connections, their monodromy, and their flat sections.