Johannes Kellendonk (University of Cardiff)
kellendonkj@cardiff.ac.uk
A convincing explanation of the Quantum Hall Effect has to include a proper treatment of disorder. This could be achieved by Bellissard using a C*-algebraic approach to disordered systems. In his model, the Hall sample is idealized as extended over the whole plane; the Hall-conductivity can then be expressed as a (non-commutative) Chern number. Other models explain the Hall-conductivity as that of a current flowing around the edge of a finite sample. We provide a link between these two approaches using the framework of K-theory and cyclic cohomology of algebras. (Joint work with Hermann Schulz-Baldes and Thomas Richter.)