What Discovering the mechanism for high-Tc superconductivity is the first step towards predicting new materials with room temperature superconductivity, a grand discovery that would potentially revolutionise our energy sector. Creating devices for quantum computation would transform our technological society, allowing for safe internet communication, and simulations of real quantum systems. Why The fundamental mechanism behind high-Tc superconductivity is unknown, and the generation and manipulation of Majorana particles is a field in its infancy. We want to understand the origin of superconductivity and predict new exotic electronic phases that host Majorana fermions useful to topological quantum computing. How The studies are theoretical investigations of both toy models and realistic simulations of actual materials and devices. We work in close collaboration with laboratories all over the world, which we help guide (and are guided).