Professor Siddharth Parameswaran gives the second talk on Axions. Over the past decade, topological ideas have played an increasingly important role in a surprising setting: the problem of understanding the properties of insulating crystals. This has led to the identification of “topological insulators”, bulk insulating materials which are characterised by unusual surface phenomena, unconventional responses to applied electric and magnetic fields, or both. In particular, the motion of electrons in some three-dimensional solids can generate axion-like electrodynamics in the solid state. He explains how the ideas leading to the prediction of this “axion insulator” flow naturally from a deeper understanding of the electrodynamics of dielectric media and their link to topological ideas, and survey some of their unusual consequences for experiment.