  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.
