Searches for $t\bar{t}H$ and flavour-changing $t\to Hq$ productions in multileptonic final states with the ATLAS detector

After the Higgs boson discovery at the Large Hadron Collider (LHC), the focus of experimental particle physics is on the measurement of its interaction with other particles of the Standard Model (SM). The interaction strength with SM fermions is determined by the Yukawa coupling, which is proportional to the particle mass and therefore the largest for the top quark. This doctoral thesis describes the search for the associated Higgs boson production with a pair of top quarks ($t\bar{t}H$) in a dataset of proton-proton collisions at a center-of-mass energy of $\sqrt{s}=$ 13 TeV and with an integrated luminosity of 36.1 fb$^{-1}$, recorded by the ATLAS detector in 2015 and 2016. Seven final states, associated to different Higgs boson decays into vector bosons or tau leptons and containing at least two leptons, are optimised to get the best signal to background separation. An excess of events over the SM background is observed with a significance of 4.1 standard deviations, while 2.8 are expected. In combination with search results obtained for other Higgs boson decay channels, the $t\bar{t}H$ production has been discovered with the ATLAS detector using up to 79.8 fb$^{-1}$ of collision data at $\sqrt{s}=$ 7, 8 and 13 TeV. Flavour-changing neutral currents in top quark decays into a Higgs boson and a light up-type quark ($t\to Hq$) are strongly suppressed in the SM. New physics models can predict a $t\to Hc$ decay branching ratio of 0.15%. The search for these decays in final states with two or three leptons observes no signal. An upper limit on the $t\to Hc$ ($t\to Hu$) decay branching ratio at a 95% confidence level is set at 0.16% (0.19%) with an expected limit of 0.15% (0.15%). To bypass the limitation of an insufficient amount of collision data, the LHC and its experiments foresee an ambitious upgrade plan. The current ATLAS Liquid Argon Calorimeter readout will be replaced to get an increased granularity to improve the trigger selectivity and avoid bandwidth saturation at high luminosity. A demonstrator system has been operated since 2015 and its performance studied with calibration and collision data.