Hilary Greaves' current research mainly concerns the notion of symmetry in physics and examines the question of what we can infer, from the symmetries of our best physical theories, about the structure of space and time, and in how (if at all) answers to such questions are different in classical and in quantum theories. At the moment she is particularly interested in time reversal and the CPT theorem, and in the foundations of quantum field theory more generally.
Before that, much of Hilary's recent research focussed on the Everett ("many-worlds") interpretation of quantum mechanics. It has often been thought that, due to conceptual difficulties that arise when one tries, quantum mechanics cannot be interpreted as even an approximately true description of physical reality; it must rather (the idea runs) be regarded as merely an algorithm for predicting the results of experiments. Against this, the Everett interpretation aims to provide a "realist" account of quantum reality. The interpretation, however, faces problems, among which is the "problem of probability": it seems difficult to make conceptual sense of the probabilistic predictions of quantum mechanics within an Everett interpretation.
Prof. Greaves' work within the program looks to examine the primary research questions by bringing to bear insights from decision theory, confirmation theory and the philosophy of probability.