The first part of this thesis presents a search for the direct pair production of supersymmetric top squarks in events containing two opposite-charge leptons (electrons or muons), jets, and missing transverse momentum. The analysis is based on proton-proton collision data collected with the ATLAS detector at the Large Hadron Collider (LHC), corresponding to a total integrated luminosity of 193 fb^-1. The search specifically targets top squarks undergoing a two-body decay into a top quark and the lightest neutralino, and it is sensitive across a wide range of mass differences between the two supersymmetric particles. Using the full dataset, the analysis achieves an expected sensitivity to top squark masses beyond 1.1 TeV, and neutralino masses up to 600 GeV. The sensitivity of the analysis is also evaluated for models in which the mass difference between the top squark and the lightest neutralino is smaller than the top quark mass. In these scenarios, the top squark decays to the lightest neutralino, and to a W boson and a b-quark via an off-shell top. For these models, the analysis sensitivity extends to neutralino masses up to 450 GeV, for top squark masses of 600 GeV. Finally, the analysis is applied to a model consisting of the associated production of top-antitop quark pairs with an invisibly decaying Higgs boson, resulting in an expected upper limit on the Higgs boson's invisible branching ratio of 0.29, based on the full 193 fb^-1 dataset.

The second part of this thesis presents the ATLAS trigger system as configured for Run 3, following a major upgrade between the Run 2 and the Run 3 data-taking periods of the LHC. Since the start of Run 3, ATLAS is recording up to 3 kHz of fully built physics events out of an LHC collision rate of 40 MHz, with additional rate allocated to partial event readout. The two-level trigger system is responsible for selecting in real time events of interest for the broad ATLAS physics programme, while rejecting a high rate of background events. The selection of events, encoded in the ATLAS trigger menu, targets both generic and analysis specific physics signatures. One of the main challenges of the ATLAS trigger system is to maximise the physics outcome of the recorded dataset while operating within strict constraints on bandwidth and CPU resources. This thesis provides a detailed overview of the high-level-trigger performance monitoring tools. A particular focus is given to the strategy for applying prescale factors to manage trigger rates and CPU usage. In this context, a central contribution of this work is the development and optimisation of the software package used to generate prescale sets for ATLAS data-taking in Run 3.