Bundle gerbes for topological insulators

Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter systems via equivariant bundle gerbes. The construction covers static and periodically driven systems with time reversal invariance in 2 and 3 space dimensions. It involves refinements of geometry of gerbes that are discussed in the first lecture, the second one being devoted to the applications to topological insulators.