My overall research program is devoted to alternative parametrizations of the gravitational field. The general theory of relativity is based upon a mathematical structure called a manifold, and my research is focused on looking at different presentations of this mathematical structure to determine if they can be used to gain a better understanding of the gravitational field.
For instance, exotic smooth structure is a unique feature of manifolds in four-dimensions, and I have proven that at least in some cases, the inclusion of exotic smooth structure can change the outcome of theoretical calculations in semiclassical gravity. In a currently ongoing program, I am looking at modeling dark matter with these exotic smooth structures. In this case, it might be that dark matter does not consist of exotic particles, but rather exotic mathematics.
Finally, I am interested in the connection between quantum mechanics and gravity, specifically that which is found in loop quantum gravity. With some collaborators, we have developed the only self-consistent approach to include topological change in loop quantum gravity.