Bershadsky–Cecotti–Ooguri–Vafa mirror symmetry conjecture

Let $M$ be a Kähler manifold, let $F_g^{\mathrm{BCOV}}(M)$ be the genus-$g$ BCOV quantity defined by summing the Cauchy principal value graph integrals over connected trivalent graphs, and let $M^{\vee}$ be a mirror manifold. For $g\ge 2$, the BCOV mirror symmetry conjecture asserts that $F_g^{\mathrm{BCOV}}(M)$ defines the genus-$g$ B-model invariant: it is independent of the Kähler class of $M$, and, when $M$ and $M^{\vee}$ are mirror manifolds, the holomorphic limit of $F_g^{\mathrm{BCOV}}(M)$ coincides with the genus-$g$ Gromov–Witten invariants of $M^{\vee}$. This conjecture gives the higher-genus B-model counterpart of mirror symmetry by identifying BCOV graph-integral invariants with Gromov–Witten theory on the mirror; the source formulates it but does not state a general resolution.