  We present spatial correlations of galaxies and IGM HI in the
COSMOS/UltraVISTA 1.62 deg$^2$ field. Our data consist of 13,415 photo-$z$
galaxies at $z\sim2-3$ with $K_s<23.4$ and the Ly$\alpha$ forest absorptions in
the background quasar spectra selected from SDSS data with no signature of
damped Ly$\alpha$ system contamination. We estimate a galaxy overdensity
$\delta_{gal}$ in an impact parameter of 2.5 pMpc, and calculate the Ly$\alpha$
forest fluctuations $\delta_{\langle F\rangle}$ whose negative values
correspond to the strong Ly$\alpha$ forest absorptions. We identify weak
evidence of an anti-correlation between $\delta_{gal}$ and $\delta_{\langle
F\rangle}$ with a Spearman's rank correlation coefficient of $-0.39$ suggesting
that the galaxy overdensities and the Ly$\alpha$ forest absorptions positively
correlate in space at the $\sim90\%$ confidence level. This positive
correlation indicates that high-$z$ galaxies exist around an excess of HI gas
in the Ly$\alpha$ forest. We find four cosmic volumes, dubbed
$A_{obs}$-$D_{obs}$, that have extremely large (small) values of $\delta_{gal}
\simeq0.8$ ($-1$) and $\delta_{\langle F\rangle}$ $\simeq0.1$ ($-0.4$), three
out of which, $B_{obs}$-$D_{obs}$, significantly depart from the correlation,
and weaken the correlation signal. We perform cosmological hydrodynamical
simulations, and compare with our observational results. Our simulations
reproduce the correlation, agreeing with the observational results. Moreover,
our simulations have model counterparts of $A_{obs}$-$D_{obs}$, and suggest
that the observations pinpoint, by chance, a galaxy overdensity like a
proto-cluster, gas filaments lying on the sightline, a large void, and
orthogonal low-density filaments. Our simulations indicate that the significant
departures of $B_{obs}$-$D_{obs}$ are produced by the filamentary large-scale
structures and the observation sightline effects.
