  We report on the result of a campaign to monitor 25 HATSouth candidates using
the K2 space telescope during Campaign 7 of the K2 mission. We discover
HATS-36b (EPIC 215969174b), a hot Jupiter with a mass of 2.79$\pm$0.40 M$_J$
and a radius of 1.263$\pm$0.045 R$_J$ which transits a solar-type G0V star
(V=14.386) in a 4.1752d period. We also refine the properties of three
previously discovered HATSouth transiting planets (HATS-9b, HATS-11b, and
HATS-12b) and search the K2 data for TTVs and additional transiting planets in
these systems. In addition we also report on a further three systems that
remain as Jupiter-radius transiting exoplanet candidates. These candidates do
not have determined masses, however pass all of our other vetting observations.
Finally we report on the 18 candidates which we are now able to classify as
eclipsing binary or blended eclipsing binary systems based on a combination of
the HATSouth data, the K2 data, and follow-up ground-based photometry and
spectroscopy. These range in periods from 0.7 days to 16.7 days, and down to
1.5 mmag in eclipse depths. Our results show the power of combining
ground-based imaging and spectroscopy with higher precision space-based
photometry, and serve as an illustration as to what will be possible when
combining ground-based observations with TESS data.
