Recent ATLAS measurements of azimuthal anisotropies in $pp$ and $p$+Pb collisions

The azimuthal anisotropies of particle yields observed in relativistic heavy-ion collisions are considered as an evidence of the formation on a deconfined Quark-Gluon Plasma produced in these collisions. Interestingly, recent measurements in $pp$ and $p$+Pb systems from ATLAS and other experiments show similar features as those observed in A+A collisions, indicating the possibility of the production of such a deconfined medium in smaller collision systems. This report presents a summary of the recent ATLAS results on azimuthal anisotropies in $pp$ collisions at 5.02~TeV and 13~TeV, $p$+Pb collisions at 5.02~TeV and 8.16~TeV as well as in peripheral 2.76~TeV Pb+Pb interactions. It includes measurements of two-particle correlations of charged particles as well as correlations of heavy flavor muons and charged particles in $\Delta\phi$ and $\Delta\eta$, with a template fitting procedure used to subtract the dijet contributions. Additionally, measurements of cumulants of multi-particle correlations, $c_{n}${2-8} are presented. The two-particle correlations and cumulants confirm a presence of collective phenomena in these collision systems, but the results on four-particle cumulants for $pp$ collisions do not demonstrate a similar collective behaviour. However, the cumulant measurements in small collision systems can be biased by ``non-flow'' correlations. A novel subevent cumulant method that suppresses the contribution of ``non-flow'' effects was proposed recently by ATLAS allowing to measure significant azimuthal anisotropies in both $pp$ and $p$+Pb collisions.