Studies of exoplanet demographics require large samples and precise constraints on exoplanet host stars. Using the homogeneous Kepler stellar properties derived using Gaia Data Release 2 by Berger et al. (2020), we re-compute Kepler planet radii and incident fluxes and investigate their distributions with stellar mass and age. We measure the stellar mass dependence of the planet radius valley to be $d log R_{mathrm{p}}$/$d log M_star = 0.26^{+0.21}_{-0.16}$, consistent with the slope predicted by a planet mass dependence on stellar mass ($0.24-0.35$) and core-powered mass-loss (0.33). We also find first evidence of a stellar age dependence of the planet populations straddling the radius valley. Specifically, we determine that the fraction of super-Earths ($1-1.8 mathrm{R_oplus}$) to sub-Neptunes ($1.8-3.5 mathrm{R_oplus}$) increases from $0.61 pm 0.09$ at young ages (< 1 Gyr) to $1.00 pm 0.10$ at old ages (> 1 Gyr), consistent with the prediction by core-powered mass-loss that the mechanism shaping the radius valley operates over Gyr timescales. Additionally, we find a tentative decrease in the radii of relatively cool ($F_{mathrm{p}} < 150 mathrm{F_oplus}$) sub-Neptunes over Gyr timescales, which suggests that these planets may possess H/He envelopes instead of higher mean molecular weight atmospheres. We confirm the existence of planets within the hot sub-Neptunian desert ($2.2 < R_{mathrm{p}} < 3.8 mathrm{R_oplus}$, $F_{mathrm{p}} > 650 mathrm{F_oplus}$) and show that these planets are preferentially orbiting more evolved stars compared to other planets at similar incident fluxes. In addition, we identify candidates for cool ($F_{mathrm{p}} < 20 mathrm{F_oplus}$) inflated Jupiters, present a revised list of habitable zone candidates, and find that the ages of single- and multiple-transiting planet systems are statistically indistinguishable.
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