My dissertation is on the relevance of calculational methods to the interpretation of scientific theories. I focus in particular on the relevance of renormalization group methods to the interpretation of quantum field theories. I argue that interpretational strategies that focus on the fundamental equations of theories and ignore actual applications are more prone to mistinterpreting the fundamental equations themselves. Furthermore, I argue that this tendency for calculational methods to alter the interpretation of the fundamental equations is a general one that often happen in the history of mathematics and physics.
Relatedly, I have worked on showing how reasoning strategies based on comparing mathematically problematic models were crucial to foundational reasoning in early quantum electrodynamics. This is published as a paper in Studies in History and Philosophy of Science Part B. You can download a preprint here.
Another ongoing project I have is an investigation of the relationship between time-independent and time-dependent treatments of quantum scattering. The idea is that the time-independent treatment is not merely an approximation to the time-dependent treatment, because the latter does not provide a "true evolution in time" story of scattering. Furthermore, the roles of what we normally take to be "laws" and "initial and boundary conditions" in these two treatments is complex and does not map on to the usual story of laws containing all nomic information and "initial and boundary conditions" containing only contingent information.