Constraining the 21cm brightness temperature of the IGM at $z$=6.6
  around LAEs with the Murchison Widefield Array
  The locations of Ly-$\alpha$ emitting galaxies (LAEs) at the end of the Epoch
of Reionisation (EoR) are expected to correlate with regions of ionised
hydrogen, traced by the redshifted 21~cm hyperfine line. Mapping the neutral
hydrogen around regions with detected and localised LAEs offers an avenue to
constrain the brightness temperature of the Universe within the EoR by
providing an expectation for the spatial distribution of the gas, thereby
providing prior information unavailable to power spectrum measurements. We use
a test set of 12 hours of observations from the Murchison Widefield Array (MWA)
in extended array configuration, to constrain the neutral hydrogen signature of
58 LAEs, detected with the Subaru Hypersuprime Cam in the \textit{Silverrush}
survey, centred on $z$=6.58. We assume that detectable emitters reside in the
centre of ionised HII bubbles during the end of reionization, and predict the
redshifted neutral hydrogen signal corresponding to the remaining neutral
regions using a set of different ionised bubble radii. A prewhitening matched
filter detector is introduced to assess detectability. We demonstrate the
ability to detect, or place limits upon, the amplitude of brightness
temperature fluctuations, and the characteristic HII bubble size. With our
limited data, we constrain the brightness temperature of neutral hydrogen to
$\Delta{\rm T}_B<$30 mK ($<$200 mK) at 95% (99%) confidence for
lognormally-distributed bubbles of radii, $R_B =$ 15$\pm$2$h^{-1}$cMpc.
