  We present results from the EDGE survey, a spatially resolved CO(1-0)
follow-up to CALIFA, an optical Integral Field Unit (IFU) survey of local
galaxies. By combining the data products of EDGE and CALIFA, we study the
variation in molecular gas depletion time ($\tau_{\rm dep}$) on kiloparsec
scales in 52 galaxies. We divide each galaxy into two parts: the center,
defined as the region within $0.1 \ R_{25}$, and the disk, defined as the
region between $0.1$ and $0.7 \ R_{25}$. We find that 14 galaxies show a
shorter $\tau_{\rm dep}$ ($\sim 1$ Gyr) in the center relative to that in the
disk ($\tau_{\rm dep} \sim 2.4$ Gyrs), which means the central region in those
galaxies is more efficient at forming stars per unit molecular gas mass. This
finding implies that the centers with shorter $\tau_{\rm dep}$ resemble the
intermediate regime between galactic disks and starburst galaxies. Furthermore,
the central drop in $\tau_{\rm dep}$ is correlated with a central increase in
the stellar surface density, suggesting that a shorter $\tau_{\rm dep}$ is
associated with molecular gas compression by the stellar gravitational
potential. We argue that varying the CO-to-H$_2$ conversion factor only
exaggerates the central drop of $\tau_{\rm dep}$.
