We propose a research project to work within the field of extreme astrophysics, on ultra-compact binaries and gamma-ray bursts. In particular we wish to understand the role of compact binaries as gamma-ray burst (GRB) progenitors, the formation of compact binaries in the field of our Galaxy and the production of interacting binaries in globular clusters. We will approach these connected problems in four different ways. First, we will predict the galactic offsets of short GRBs, using our detailed binary stellar evolution code to compute the evolution of the binaries most important for their production. Some events in compact binary evolution that proceed on hydrodynamical timescales will be modelled using smoothed particle hydrodynamics (SPH). We shall further use the predictions to model the wind outflows from the binary and single-star progenitors of long gamma-ray bursts to determine if the two can be distinguished. Secondly, we shall use a detailed stellar evolution code to compute the evolution of ultra-compact binaries in the field, to better understand the origins of some of their observed properties. Thirdly, we shall use a code that combines detailed stellar evolution and N-body dynamics to model the evolution of the progenitor binaries of gamma-ray bursts in dense stellar environments. Finally, we shall estimate the production rate of LISA-visible binaries in the field and in globular clusters from the models mentioned above. To achieve this scientific programme we intend to recruit Ross Church as a fellow. Church is an expert in stellar evolution and N-body dynamics, and his computer code that combines the two is a unique research tool for the investigation of stellar evolution in dense stellar systems such as the core of a globular cluster. His recruitment will broaden his scientific skill base and research interests and allow him to mature as a researcher, thus fulfilling the aims of the FP7 "people" work programme.