In my research, I have applied mathematical techniques such as homology, catastrophy, integral geometry and Picard-Lefschetz theory to problems in cosmology. I have applied these techniques to the formation and properties of the cosmic microwave background radiation field, the formation of the large-scale structure and the study of the big bang in Lorentzian quantum cosmology. In my work, I attempt to study observable phenomena, using conservative assumptions in a critical and mathematically rigorous fashion. See links below for a summary of my main projects.