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A search for flavour-changing neutral current (FCNC) events via the couplingof a top quark, a photon, and an up or charm quark is presented using 81fb$^{-1}$ of proton-proton collision data taken at a centre-of-mass energy of13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron ormuon, a $b$-tagged jet, and missing transverse momentum are selected. A neuralnetwork based on kinematic variables differentiates between events from signaland background processes. The data are consistent with the background-onlyhypothesis, and limits are set on the strength of the $tq\gamma$ coupling in aneffective field theory. These are also interpreted as 95% CL upper limits onthe cross section for FCNC $t\gamma$ production via a left-handed(right-handed) $tu\gamma$ coupling of 36 fb (78 fb) and on the branching ratiofor $t\rightarrow \gamma u$ of $2.8\times 10^{-5}$ ($6.1\times 10^{-5}$). Inaddition, they are interpreted as 95% CL upper limits on the cross section forFCNC $t\gamma$ production via a left-handed (right-handed) $tc\gamma$ couplingof 40 fb (33 fb) and on the branching ratio for $t\rightarrow \gamma c$ of$22\times 10^{-5}$ ($18\times 10^{-5}$).

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Search for flavour-changing neutral currents in processes with one top  quark and a photon using 81 fb$^{-1}$ of $pp$ collisions at $\sqrt{s} = 13$  TeV with the ATLAS experiment