This line of research currently includes: study of properties and applications of random matrices, focusing on the distribution of polynomial functions over Lie groups, applied to scattering matrices that describe wave propagation in chaotic systems; study of quantum phase transitions in ordered and disordered systems; study of measurement theory in quantum mechanics, in addition to von Neumann's scheme, in particular of weak measurement with post-selection; Lorentz transformations for non-inertial observers in special and general relativity.