Counting positive-genus real curves
I will present an overview of the (complex) Gromov-Witten invariants and their relation to curve counts provided by the Gopakumar-Vafa formula for Fano classes. I will then present a similar formula that transforms the real postive-genus GW-invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. Joint work with A. Zinger.