The field of topological phases, phases that are characterized by a topological invariant, or described by a topological field theory (or both) have witnessed a recent resurgence in interest. I have worked on general aspects of the theory, including the topological classification of insulators and superconductors and continue to be interested in topological insulators and superconductors and also specifically in Strontium Ruthenate, the most promising candidate material for a topological superconductor. I have also been interested in more general topological aspects of condensed matter physics, such as in the understanding of adiabatic cycles and of the constraints placed by space group symmetries on ground state degeneracies. Some of my other recent work is on the yet to be experimentally realized fractional Chern insulators, which are phases that emerge in fractionally filled Chern bands in the presence of short range interactions
