Understanding the strongly correlated states of matter, where the properties of a many body system are dominated by quantum effects, is one of the grand challenges of modern science. It lies at the origin of spectacular new phenomena, such as unconventional superconductivity and magnetic monopoles, and underpins new technologies, such as portable batteries and thermoelectrics. Recent investments in ISIS and the Diamond Light Source on the nearby Harwell Campus make them the leading UK facilities for physical sciences for the next twenty years. We have opportunities for PhD projects that exploit these facilities for the study of the lattice dynamics of thermoelectrics, ion diffusion of battery materials, superstructures in iron-based superconductors, and defect structures in spin ice. The training ranges from single-crystal and thin-film growth, structure determination using neutron and x-ray diffraction, physical property measurement, the study of excitations using inelastic neutron and synchrotron x-ray scattering, to modelling using first-principles density-functional theory.