We present a detailed investigation of the Large Magellanic Cloud (LMC) disk using classical Cepheids. Our analysis is based on optical (I,V ; OGLE-IV), near-infrared (NIR: J,H,K S ) and midinfrared (MIR: w1; WISE) mean magnitudes. By adopting new templates to estimate the NIR mean magnitudes from single-epoch measurements, we build the currently most accurate, largest and homogeneous multi-band dataset of LMC Cepheids. We determine Cepheid individual distances using optical and NIR Period-Wesenheit relations (PWRs), to measure the geometry of the LMC disk and its viewing angles. Cepheid distances based on optical PWRs are precise at 3%, but accurate to 7%, while the ones based on NIR PWRs are more accurate (to 3%), but less precise (2%-15%), given the higher photometric error on the observed magnitudes. We found an inclination i=25.05 ± 0.02 (stat.) ± 0.55 (syst.) deg, and a position angle of the lines of nodes P.A.=150.76 ± 0.02 (stat.) ± 0.07 (syst.) deg. These values agree well with estimates based either on young (Red Supergiants) or on intermediate-age (Asymptotic Giant Branch, Red Clump) stellar tracers, but they significantly differ from evaluations based on old (RR Lyrae) stellar tracers. This indicates that young/intermediate and old stellar populations have different spatial distributions. Finally, by using the reddening-law fitting approach, we provide a reddening map of the LMC disk which is ten times more accurate and two times larger than similar maps in the literature. We also found an LMC true distance modulus of µ 0,LM C = 18.48 ± 0.10 (stat. and syst.) mag, in excellent agreement with the currently most accurate measurement (Pietrzyński et al. 2013).

New accurate and homogeneous optical UBVRI photometry has been obtained for variable stars in the Galactic globular cluster ω Cen (NGC 5139). We secured 8202 CCD images covering a time interval of 24 years and a sky area of 84×48 arcmin. The current data were complemented with data available in the literature and provided new, homogeneous pulsation parameters (mean magnitudes, luminosity amplitudes, periods) for 187 candidate ω Cen RR Lyrae (RRLs). Among them we have 101RRc (first overtone) and 85RRab (fundamental) variables, and a single candidate RRd (double-mode) variable. Candidate Blazhko RRLs show periods and colors that are intermediate between the RRc and RRab variables, suggesting that they are transitional objects. A comparison of the period distribution and the Bailey diagram indicates that RRLs in ω Cen show a long-period tail not present in typical Oosterhoff II (OoII) globulars. The RRLs in dwarf spheroidals and in ultra-faint dwarfs have properties between Oosterhoff intermediate and OoII clusters. Metallicity plays a key role in shaping the above evidence. These findings do not support the hypothesis that ω Cen is the core remnant of a spoiled dwarf galaxy. Using optical period-Wesenheit relations that are reddening-free and minimally dependent on metallicity we find a mean distance to ω Cen of 13.71±0.08±0.01 mag (semi-empirical and theoretical calibrations). Finally, we invert the I-band period-luminosity-metallicity relation to estimate individual RRLs' metal abundances. The metallicity distribution agrees quite well with spectroscopic and photometric metallicity estimates available in the literature.