Twisted crossed products, Kasparov theory and the bulk-edge correspondence of topological phases

par Chris Bourne (Friedrich-Alexander-Universität Erlangen-Nürnberg)

vendredi 25 mars 2016, 14:00 → 15:00 Europe/Paris

salle Fokko du Cloux (Institut Camille Jordan)

The C*-algebraic approach to of condensed matter physics, spearheaded by Jean Bellissard, has proven to be an effective tool to accurately model the topological properties of certain systems, e.g. the quantum Hall effect. In this talk we consider so-called topological insulators, which may contain anti-linear symmetries and can give rise to torsion invariants. We show that Bellissard's framework for studying such systems remains valid with certain adjustments that account for the anti-linear symmetries. Namely we work under Kasparov's bivariant K-theory for real or complex C*-algebras. We aim to explain this process with minimal assumed knowledge of physics or Kasparov theory. This is joint work with J. Kellendonk and A. Rennie (University of Wollongong).