The Standard Model (SM) is a theory which accurately describes the elementary constituents of matter and interactions between them at the energy scales we have been able to probe in experiments up to the present day. However, since in the Nature we observe physics phenomena beyond the SM, it is expected that the SM is a low-energy effective approximation of a theory that describes the physics of particles and their interactions in a broader way. Lorentz Invariance is a fundamental symmetry of the SM, but it is not expected to be conserved necessarily at the high energy scale of quantum gravity where space-time could undergo violent fluctuations. The violation of the Lorenz invariance (LIV), which is predicted by some extensions of the SM theory, would manifests itself at energies accessible by the experiments nowadays. I propose to preform the first search for the possible LIV in the top quark interactions at the ATLAS experiment at CERN’s Large Hadron Collider (LHC) that will pioneer the use of innovative approaches to analyse collision data taking into account detector orientation in the space-time continuum. The project will comprise phenomenological study to identify observables most sensitive to LIV, development of the novel framework for analysing data as a function of the sidereal time, study of the time-dependence of the ATLAS detector performance and state-of-the-art collision data analysis. My long-standing experience with measurements targeting the final states with top quarks and Higgs boson decays, provide me with unique expertise to perform this search and unlock the hidden potential of the LHC collision data. In addition, I plan to use my expertise in the jet flavour tagging and further improve the performance of the b-jet tagging algorithms for the upcoming LHC Run-3 data-taking period. My knowledge, skills and technical expertise gained over the course of last several years, supported by the extensive expertise in the key areas of IPB and CERN teams

Transport in strongly correlated materials is one of the central topics in condensed matter physics. Due to major prospects for technological applications, particular attention is paid to the cuprate superconductors, and by association, to kappa-organic materials and moiré systems. The last decade has seen great progress in the understanding of the generic high-temperature properties of these systems, largely based on the microscopic yet simplified interacting lattice models. However, there are multiple outstanding questions regarding their low-temperature physics. The mechanism of the strange-metallic linear-in-temperature resistivity and its relation to superconductivity have so far eluded understanding. There is conflicting evidence for the quantum critical (QC) scenario, which is a common view that there is a zero-temperature QC point hidden behind the superconducting dome on the phase diagram of the cuprates. Recent magnetoresistance measurements in these and other materials contribute to a puzzling phenomenology. The factors that determine the magnitude of the superconducting critical temperature are also poorly understood. Further progress is blocked by the limitations of quantum many-body numerical methods. To address these questions, we propose to employ a highly promising new approach to the numerical solution of the many-electron problem. It may overcome the long-standing limitations and allow for an unprecedented accuracy and control. The real-frequency diagrammatic Monte Carlo method will yield numerically exact results for the resistivity in a range of lattice models, at low temperature, and as a function of magnetic field. These results will help interpret recent experimental results, set new predictions, and open doors to reverse-engineering of functional materials. The tools we develop will be readily applicable to a wide range of condensed matter physics problems, and we will make all code packages publicly available.