Comparing local and log GW invariants

Let $X$ be a smooth projective variety and let $D$ be a smooth nef divisor on it. In this collaboration
with Tom Graber and Helge Ruddat, we show that the genus $0$ local Gromov-Witten (GW) invariants
of the total space of $\mathcal{O}(-D)$ equal, up to a factor, the genus $0$ log GW invariants of $X$
with a single condition of maximal contact order along $D$.