This allows us to take into account the local timezone -- any days where
all the events were outside the local 24-hour period are the ones that
are empty.
Since we're rendering according to the local timezone, we'll need to
include events that fall before or after the specific date on the
server, as they might get be inside the current day in the client's
timezone. So let's just grab a window of events either side of today,
and then hide anything that falls outside the client's day.