Curved spaces are usually associated with high-energy physics and cosmology. However, through the possibility of tabletop experiments emulating curved spaces and the interest in related synthetic matter, they have become relevant in condensed matter physics as well.
After the experimental discovery of topological insulators, the notion of what actually constitutes a topological band insulator has been refined in many ways. In their recent work, Aleksandra Nelson, Titus Neupert, Tomáš Bzdušek and Aris Alexandradinata extend the paradigm of topological insulators to areas which were previously thought to contain only trivial insulators.
Electron band structures, which describe the energy-momentum relation for electrons in solids, can exhibit robust crossings called "nodes". Such nodes famously occur in graphene or in Weyl semimetals, and often facilitate special transport phenomena, such as the decrease of resistivity of Weyl semimetals in applied parallel magnetic field.