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We present spatial correlations of galaxies and IGM HI in theCOSMOS/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 inthe background quasar spectra selected from SDSS data with no signature ofdamped 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 valuescorrespond to the strong Ly$\alpha$ forest absorptions. We identify weakevidence of an anti-correlation between $\delta_{gal}$ and $\delta_{\langleF\rangle}$ with a Spearman's rank correlation coefficient of $-0.39$ suggestingthat the galaxy overdensities and the Ly$\alpha$ forest absorptions positivelycorrelate in space at the $\sim90\%$ confidence level. This positivecorrelation indicates that high-$z$ galaxies exist around an excess of HI gasin 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 $\delta_{\langle F\rangle}$ $\simeq0.1$ ($-0.4$), threeout of which, $B_{obs}$-$D_{obs}$, significantly depart from the correlation,and weaken the correlation signal. We perform cosmological hydrodynamicalsimulations, and compare with our observational results. Our simulationsreproduce the correlation, agreeing with the observational results. Moreover,our simulations have model counterparts of $A_{obs}$-$D_{obs}$, and suggestthat the observations pinpoint, by chance, a galaxy overdensity like aproto-cluster, gas filaments lying on the sightline, a large void, andorthogonal low-density filaments. Our simulations indicate that the significantdepartures of $B_{obs}$-$D_{obs}$ are produced by the filamentary large-scalestructures and the observation sightline effects.

Cosmic Galaxy-IGM HI Relation at ${\it{z}}\sim 2-3$ Probed in the COSMOS/UltraVISTA $1.6$ deg$^2$ Field