Recent results on associated top-quark production and searches for new top-quark phenomena with the ATLAS detector

The high center-of-mass energy of proton-proton collisions and the large available datasets at the CERN Large Hadron Collider allow to study rare processes of the Standard Model (SM) with unprecedented precision and search for new physics that might enhance extremely rare processes in the SM. Measurements of rare SM processes provide new tests of the SM predictions with the potential to unveil discrepancies with the SM predictions or provide important input for the improvement of theoretical calculations. Interesting processes are Flavour Changing Neutral Currents (FCNC): forbidden at tree level and highly suppressed at higher orders in the Standard Model (SM), FCNC processes can receive enhanced contributions in many extensions of the SM, so any measurable sign of such interactions is an indication of new physics. In this talk, total and differential measurements of top-quark production in association with additional bosons are shown using data taken with the ATLAS experiment at a center-of-mass-energy of 13 TeV. The recent observation of associated production of a single top quark with a photon completes the list of processes and adds sensitivity to the EW couplings of the top quark, while measurements of production asymmetries in various final states provide further precision tests of the SM. In addition, new searches for charged lepton flavour violation and FCNCs with the ATLAS experiment are shown, using the full data taken during Run-2 of the LHC, as well as other searches for beyond-the-Standard-Model phenomena in top-quark final states.