  Recent exact solutions of the 1D Kardar-Parisi-Zhang equation make use of the
1D integrable Lieb-Liniger model of interacting bosons. For flat initial
conditions, it requires the knowledge of the overlap between the uniform state
and arbitrary exact Bethe eigenstates. The same quantity is also central in the
study of the quantum quench from a 1D non-interacting Bose-Einstein condensate
upon turning interactions. We compare recent advances in both domains, i.e. our
previous exact solution, and a new conjecture by De Nardis et al.. This leads
to new exact results and conjectures for both the quantum quench and the KPZ
problem.
