We present the first results from the GeMS/GSAOI Galactic Globular Cluster Survey (G4CS) of the Milky-Way globular clusters (GCs) NGC 3201 and NGC 2298. Using the Gemini South Adaptive Optics Imager (GSAOI), in tandem with the Gemini Multi-conjugate adaptive optics System (GeMS) on the 8.1-meter Gemini-South telescope, we collected deep near-IR observations of both clusters, resolving their constituent stellar populations down to $K_ssimeq21$ Vega mag. Point spread function (PSF) photometry was performed on the data using spatially-variable PSFs to generate $JHK_{s}$ photometric catalogues for both clusters. These catalogues were combined with Hubble Space Telescope (HST) data to augment the photometric wavelength coverage, yielding catalogues that span the near-ultraviolet (UV) to near-infrared (near-IR). We then applied 0.14 mas/year accurate proper-motion cleaning, differential-reddening corrections and chose to anchor our isochrones using the lower main-sequence knee (MSK) and the main-sequence turn-off (MSTO) prior to age determination. As a result of the data quality, we found that the $K_{s}$ vs. F606W$-K_{s}$ and F336W vs. F336W$-K_{s}$ color-magnitude diagrams (CMDs) were the most diagnostically powerful. We used these two color combinations to derive the stellar-population ages, distances and reddening values for both clusters. Following isochrone-fitting using three different isochrone sets, we derived best-fit absolute ages of $12.2pm0.5$ Gyr and $13.2pm0.4$ Gyr for NGC 3201 and NGC 2298, respectively. This was done using a weighted average over the two aforementioned color combinations, following a pseudo-$chi^2$ determination of the best-fit isochrone set. Our derived parameters are in good agreement with recent age determinations of the two clusters, with our constraints on the ages being or ranking among the most statistically robust.
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