Local version of the spectral curve topological recursion

We explain a version of the topological recursion procedure of Eynard and Orantin for a collection of isolated local germs of the spectral curve. Under some conditions we can identify the n-point functions computed from spectral curve with the Givental formula for the ancestor formal Gromov-Witten potential. In particular, this way we prove a conjecture of Norbury and Scott on a particular spectral curve reproducing the stationary sector of the Gromov-Witten theory of the projective line.
The talk is based on a joint work with P. Dunin-Barkowski, N. Orantin, and L. Spitz.