We present an estimate of the absolute age of 68 galactic globular clusters obtained by exploiting the distribution of stars in the full color-magnitude diagram. In particular, we jointly estimate the absolute age, distance, reddening, metallicity ([Fe/H]) and [$alpha$/Fe] of each cluster, imposing priors motivated by independent observations; we also estimate possible systematics from stellar modeling. Our derived distances for the globular cluster sample are in agreement with those obtained from GAIA using main-sequence dwarf stars (where available), and the inferred ages are in good agreement with those previously published. The novelty of our approach is that, with the adopted priors, we are able to estimate robustly these parameters from the globular cluster color-magnitude diagram. We find that the average age of the oldest globular clusters is $t_{rm GC}=13.32 pm 0.1 {rm (stat.)} pm 0.5 {rm (sys.)}$, at 68% confidence level, including systematic uncertainties from stellar modeling. These measurements can be used to infer the age of the Universe, largely independently of the cosmological parameters: we find an age of the Universe $t_{rm U}=13.5^{+0.16}_{-0.14} {rm (stat.)} pm 0.5 ({rm sys.})$ at 68% confidence level, accounting for the formation time of globular clusters and its uncertainty. This value is compatible with $13.8 pm 0.02$ Gyr, the cosmological model-dependent value inferred by the Planck mission assuming the $Lambda$CDM model.
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