Searches for new physics with the ATLAS experiment

The Standard Model has granted exquisite power to predict the behaviour of high-energy particle collisions. It is not, however, without conceptual and empirical weaknesses. Several theories have been proposed which aim to resolve these difficulties. This thesis describes searches for twosuch theories: models of extra spatial dimensions, and supersymmetry.The Large Hadron Collider has extended the frontiers of energy and intensity in particle physics. In 2015, the LHC resumed proton–proton collisions at a centre-of-mass energy of 13 TeV. This increase over previous operation grants an enhancement in sensitivity to many processes beyond those of the Standard Model.Extra-dimensional theories address the hierarchical nature of the Standard Model. The lowered fundamental scale of gravity in these models allows a rich phenomenology at energies which may be accessible to the LHC. Some models predict the formation of microscopic black holes, which are the target of an analysis of collisions recorded by the ATLAS detector in 2015. No significant deviations from Standard Model predictions were observed. The constraints inferred on the parameters of the model are a significant advance on previous results.Lepton flavour is conserved in the Standard Model. This is not the result of a known fundamental symmetry, however. The latter part of this thesis proposes a search examining asymmetries of charge and flavour in the eμ final state. Models of supersymmetry with an R-parity-violating $\lambda'_{231}$ coupling are taken as motivation. The strategy is developed using collision data recorded by ATLAS in 2015 and 2016, and the most significant biasing effects are addressed.