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Despite the importance of feedback from active galactic nuclei (AGNs) in models of galaxy evolution, observational constraints on the influence of AGN feedback on star formation remain weak. To this end, we have compared the star formation trends of 279 low-redshift AGN galaxies with 558 inactive control galaxies using integral field unit spectroscopy from the SDSS-IV MaNGA survey. With a Gaussian process-based methodology, we reconstruct nonparametric star formation histories in spatially resolved spaxels covering the face of each galaxy. Based on galaxy-wide star formation rates (SFRs) alone, we find no obvious signatures of AGN feedback. However, the AGN galaxies have significantly suppressed central (kiloparsec-scale) SFRs, lying up to a factor of $2$ below those of the control galaxies, providing direct observational evidence of AGN feedback suppressing star formation. The suppression of central SFRs in the AGN galaxies began in the central regions ${\sim} 6$ Gyr ago (redshift $z {\sim} 0.7$), taking place over a few gigayears. A small subset of the AGN galaxies were rapidly driven to quiescence shortly before being observed (in the last $500$ Myr), potentially indicating instances of AGN-driven feedback. More frequently, however, star formation continues in the AGN galaxies, with suppression primarily in the central regions. This is suggestive of a picture in which integrated (Gyr-timescale) AGN feedback can significantly affect central star formation, but may be inefficient in driving galaxy-wide quenching in low-redshift galaxies, instead leaving them in the green valley., Comment: 22 pages, 15 figures. Accepted for publication in ApJ

The Planck list of high-redshift source candidates (the PHz catalogue) contains 2151 peaks in the cosmic infrared background, unresolved by Planck's 5 arcmin beam. Follow-up spectroscopic observations have revealed that some of these objects are $z \approx 2$ protoclusters and strong gravitational lenses, but an unbiased survey has not yet been carried out. To this end, we have used archival Herschel-SPIRE observations to study a uniformly-selected sample of 187 PHz sources. In contrast with follow-up studies that were biased towards bright, compact sources, we find that only one of our PHz sources is a bright gravitationally-lensed galaxy (peak flux $\gtrsim 300$ mJy), indicating that such objects are rarer in the PHz catalogue than previously believed ($< 1$ per cent). The majority of our PHz sources consist of many red, star-forming galaxies, demonstrating that typical PHz sources are candidate protoclusters. However, our new PHz sources are significantly less bright than found in previous studies and differ in colour, suggesting possible differences in redshift and star-formation rate. Nonetheless, 40 of our PHz sources contain $> 3\sigma$ galaxy overdensities, comparable to the fraction of $> 3\sigma$ overdensities found in earlier biased studies. We additionally use a machine-learning approach to identify less extreme (peak flux $\sim 100$ mJy) gravitationally-lensed galaxies among Herschel-SPIRE observations of PHz sources, finding a total of seven candidates in our unbiased sample, and 13 amongst previous biased samples. Our new uniformly-selected catalogues of $> 3\sigma$ candidate protoclusters and strong gravitational lenses provide interesting targets for follow up with higher-resolution facilities, such as ALMA and JWST., Comment: 23 pages, 19 figures, 4 tables. Accepted for publication in MNRAS