In the group of Prof. Guy Moore we take an interest in thermal Quantum Chromodynamics (QCD) under extreme conditions. We study heavy-ion collisions and transport coefficients in strong-interaction matter such as the viscosity, conductivity, and sphaleron rate (the diffusion coefficient for the topological charge density). We also study the topological properties of QCD matter under extremes of temperature and of baryon number and isospin chemical potentials µ_B and µ_I. We also carry out research in the field of axion cosmology and investigate the role of the topological susceptibility χ of QCD (the mean-squared fluctuations in the topology per unit spacetime volume) which determines the axion’s mass and plays a central role in its dynamics. In our research we employ various analytical and numerical methods, both in perturbative and non-perturbative QCD, and perform extensive simulations in lattice QCD.