Exploring the Limits of the Standard Model with the ATLAS Experiment at the LHC

The high-energy proton-proton collisions at the Large Hadron Collider at CERN provide a unique environment to address open questions in the fundamental description of matter and its interactions: the Standard Model. These collisions are the most likely place on Earth to produce massive particles beyond the Standard Model and to observe them with detectors such as the ATLAS experiment. The work presented in this thesis describes the exploration of two different beyond the Standard Model signatures in a supersymmetric framework, using the full Run$\,$2 dataset of 140$\,$fb$^{−1}$ proton-proton collisions at $\sqrt{s}$ = 13$\,$TeV. The first is a third-generation squark-pair decaying to a final state with one top-quark, one bottom-quark, and missing transverse energy. The second targets pair-produced gluinos that decay to an all-hadronic final state via an R-parity-violating coupling. Despite the use of dedicated search strategies, including standard cut-and-count methods and machine learning, no deviation from the Standard Model prediction is observed. The non-observation in the data constrains the lower limits on the masses of the supersymmetric particle up to 2.2$\,$TeV for gluinos at the 95% confidence level. The third-generation squark analysis gives expected exclusion limits up to 1.0$\,$TeV for the squark masses. In preparation for the extended lifetime of the Large Hadron Collider through the High-Luminosity phase, the ATLAS experiment will upgrade its tracking detector with a new, all-silicon Inner Tracker. Dedicated irradiation studies were performed at the Bern cyclotron on service components for the Inner Tracker Pixel data transmission chain. The tests presented in this thesis show that the components can withstand the total ionising dose expected for the lifetime of the High Luminosity phase and recommendations for their use are given. The results from the various studies presented in this thesis highlight the importance of continuing the exploration of beyond the Standard Model physics such as supersymmetry at the Large Hadron Collider, using the increasing statistics of the forthcoming High-Luminosity Large Hadron Collider.