From wall structures to closed mirror symmetry. The case of $K_{{\mathbb{P}}^2}$: Renormalized periods over the positive real locus, closed Gromov-Witten invariants from wall functions, and tropical enumeration

Michel van Garrel, Bernd Siebert

We recover closed Gromov-Witten invariants and renormalized mirror periods for $K_{{\mathbb{P}}^2}$ by the same operation on a wall function. This gives a direct passage from the Gro…