  The interaction of galaxies with their environment, the Intergalactic Medium
(IGM), is an important aspect of galaxy formation. One of the most fundamental,
but unanswered questions in the evolution of galaxies is how gas circulates in
and around galaxies and how it enters the galaxies to support star formation.
We have several lines of evidence that the observed evolution of star formation
requires gas accretion from the IGM at all times and on all cosmic scales. This
gas remains largely unaccounted for and the outstanding questions are where
this gas resides and what the physical mechanisms of accretion are. The gas is
expected to be embedded in an extended cosmic web made of sheets and filaments.
Such large-scale filaments of gas are expected by cosmological numerical
simulations, which have made significant progress in recent years. Such
simulations do not only model the large scale structure of the cosmic web, but
also investigate the neutral gas component. To truly make significant progress
in understanding the distribution of neutral hydrogen in the IGM, column
densities of NHI=10^18 cm-2 and below have to be probed over large areas on the
sky at sub-arcminute resolution. These are the densities of the faintest
structures known today around nearby galaxies, though mostly found with single
dish telescopes which do not have the resolution to resolve these structures
and investigate any kinematics. Existing interferometers lack the collecting
power or short baselines to achieve brightness sensitivities typically below
NHI=10^19 cm-2. Reaching lower column densities with current facilities is
feasible, however requires prohibitively long observing times. The SKA will for
the first time break these barriers, enabling interferometric observations an
order of magnitude deeper than current interferometers and with an order of
magnitude better linear resolution than single-dish telescopes.
