Non-commutative Geometry of the Quantum Hall Effect

Non-commutative geometry (NCG) provides for an extension of Bloch theory (BT) to non-commutative groups, arbitrary magnetic flux, and random disorder. This allows to carry over the topological interpretation of the Quantum Hall Effect (QHE) to all these cases, thus explaining the amazing stability of the QHE.

For the talk I assume no prior knowledge of NCG. Familiarity with BT and the QHE helps to digest the rapid review that we start with. We learn the basic ideas of NCG from simple examples. Then we review BT in this perspective. For the description of the QHE we choose a simplified approach (NCBT). It does not include disorder, but is able to deal with arbitrary magnetic flux. It is easier to grasp than the approaches in the standard literature but shows already the full power of NCG.