Lower Bounds for Enumerative Counts of Positive-Genus Real Curves

We transform the positive-genus real Gromov-Witten 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. We conclude with some implications and related conjectures for one- and two-partition Hodge integrals.