Twisted equivariant $\mathrm{K}$-theory and topological phases

Appears in collection : Spectral theory of novel materials / Théorie spectrales des nouveaux matériaux

The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real $\mathrm{K}$-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner’s theorem, is introduced by Freed and Moore by using a generalization of twisted $\mathrm{K}$-theory. In this talk, we introduce the definition of twisted $\mathrm{K}$-theory in the sense of Freed-Moore for $C^²$-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 $\mathrm{K}$-theory of operator algebras such as inductions and the Green-Julg isomorphism for the study of topological phases.

Information about the video

Date of recording 19/04/2016
Date of publication 04/05/2016
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18962503
Cite this video Kubota, Yosuke (19/04/2016). Twisted equivariant $\mathrm{K}$-theory and topological phases. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18962503
URL https://dx.doi.org/10.24350/CIRM.V.18962503