Abstract :

There is a growing interest in applying ideas of topology to understand the phases of quantum matter. In this talk we will first briefly describe the physical systems that motivate this interest, namely, quantum Hall fluids, quantum spin liquids and topological insulators. We will then review the origin of these ideas from the theory of the quantum Hall effect and trace their evolution which led to the topological characterization of the phases of quantum matter. Finally, we will present some of our work in this area.