Search for supersymmetry with the ATLAS detector at the Large Hadron Collider in final states with two hadronically decaying $\tau$-leptons

In this thesis I present all the work that I have done during my PhD. First, I will present the search for the supersymmetric partner of the $\tau-$lepton in 13 TeV proton-proton collisions at the LHC using data collected between 2015 and 2018 by the ATLAS detector. This search uses events with two hadronically decaying $tau-$leptons and missing transverse momentum in the final states. In this analysis I have been responsible for the signal region optimisation, the optimisation of the triggers and the theory systematic calculation. Results were interpreted considering natural supersymmetric extensions to the standard model in the $R$-parity conserving decays. No significant excess was observed and stringent exclusion limits were set. During my PhD I have also had leading involvement in the characterisation of the performances of the Inner Detector Trigger, which I will discuss in this thesis. Finally, stemming from my analysis work, I had major involvement in the study of a novel technique for estimating the contribution of mis-identified $tau-$leptons in signal enriched regions. A tool using this technique is currently under development in the ATLAS collaboration, that will become ATLAS approved in the very near future.