My work focuses on understanding exotic phases of matter -  phases which are not described by the conventional Landau classification based on broken symmetries. This encompasses topologically ordered phases, such as the fractional quantum Hall states in which the low-energy excitations are neither fermions nor bosons, but have "fractional" statistics. It also includes symmetry-protected phases, such as topological insulators, where unusual properties arise at the surface or boundary of the system. Two of my main foci are understanding the phase diagrams and phase transitions of these systems, and in identifying the possible types of exotic phases in 3 dimensions. These are big questions, which my research addresses by studying specific examples, often through identifying models whose behavior we can understand analytically. For example, I have been involved in studying 3D models whose surfaces are topologically ordered, some of which realize new symmetry-protected phases of matter.