Yosuke Kubota : Twisted equivariant K-theory and topological phases

Abstract: The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real K-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner&theorem, is introduced by Freed and Moore by using a generalization of twisted K-theory. In this talk, we introduce the definition of twisted K-theory in the sense of Freed-Moore for C∗-algebras, which gives a framework for the study of topological phases of non-periodic systems with a symmetry of quantum mechanics. Moreover, we introduce uses of basic tools in K-theory of operator algebras such as inductions and the Green-Julg isomorphism for the study of topological phases. Recording during the thematic meeting: "Spectral theory of novel materials" the April 19, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area