Twisted equivariant K-theory and topological insulators

This talk continues the theme of last week. The objective is to discuss the isomorphism between reduced topological phases of gapped systems with given extended quantum symmetries and twisted equivariant K-theory groups assigned the Brillouin torus. The special case of time-reversal symmetry for topological insulators will be discussed. In  particular, the Kane-Mele invariant that identifies topological insulators will be realised as a class in Real K-theory of the Brillouin torus.