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HATS-36b and 24 other transiting/eclipsing systems from the HATSouth - K2 Campaign 7 program

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.