The most effective means of understanding strongly-interacting fundamental particles, such as quarks and gluons, is via numerical simulation of lattice QCD, a discrete formulation of quantum field theory, using state-of-the-art high performance computing. Working within the Swansea Lattice Field Theory group, and as part of the international FASTSUM collaboration, the PhD student will apply these techniques to one of a range of problems: our interests include excitations in the hot medium present in the first moments of the Universe and now briefly recreated in collisions between highly relatiyistic nuclei; theories of symmetry breaking in which the Higgs is not fundamental but rather a composite strongly-bound state; theories with a non-zero particle density applicable to the dense material found within nuclei and in neutron star cores; and theories of relativistic fermions moving in a two-dimensional plane, with applications to condensed matter /materials physics to systems such as topological insulators and graphene.