  We study the signatures of reionization and ionizing properties of the early
galaxies in the cross-correlations between the 21cm emission from the spin-flip
transition of neutral hydrogen (HI) and the underlying galaxy population, in
particular a sub-population of galaxies visible as Lyman Alpha Emitters (LAEs).
With both observables simultaneously derived from a $z\simeq6.6$ hydrodynamical
simulation (GADGET-2) snapshot post-processed with a radiative transfer code
(pCRASH) and a dust model, we perform a parameter study and aim to constrain
both the average intergalactic medium (IGM) ionization state ($1-\langle
\chi_{HI} \rangle$) and the reionization topology (outside-in versus
inside-out). We find that in our model LAEs occupy the densest and most-ionized
regions resulting in a very strong anti-correlation between the LAEs and the
21cm emission. A 1000h SKA-LOW1 - Subaru Hyper Suprime Cam experiment can
provide constraints on $\langle \chi_{HI} \rangle$, allowing us to distinguish
between IGM ionization levels of 50%, 25%, 10% and fully ionized at scales
$r<10$ comoving Mpc (assuming foreground avoidance for SKA). Our results
support the inside-out reionization scenario where the densest knots
(under-dense voids) are ionized first (last) for $\langle \chi_{HI} \rangle >=
0.1$. Further, 1000h SKA-LOW1 observations should be able to confirm the
inside-out scenario by detecting a lower 21cm brightness temperature (by about
2-10 mK) in the densest regions ($> 2$ arcminute scales) hosting LAEs compared
to lower-density regions devoid of them.
