My research focuses on the search for a quantum theory of gravity (QG), and foundational questions in quantum mechanics that relate to that. I have most recently been interested in "causal dynamical triangulations", in which spacetimes are approximated using "gluings" of equilateral triangles (or tetrahedra, etc.), making it possible to define a QG theory and find some physically relevant observable quantities by computer simulations. I have benn involved with reformulating this theory in 2 dimensions, and in investigating whether the theory approximates to Einstein's theory of gravity in the appropriate regime, using simulations. I am also working on the causal set approach, in which spacetime is replaced at a more fundamental level by a discrete set of ``elements'' distinguished only by their causal relations with one another. I have been searching for observational consequences of this hypothesis. In foundations, I have been investigating definitions of causality and how they relate to quantum theory in the light of Bell's theorem.