An Introduction to the Quantum Hall Effect

Marius Wesle 

The Quantum Hall Effect, discovered 1980, is a quantised version of the classical Hall Effect. Its discovery has sparked many new ideas and revolutionised our understanding of condensed matter systems. Research directly related to the Quantum Hall Effect was awarded at least 3 Nobel Prizes, yet it is far from being fully understood and is the subject of ongoing Research.
   In this talk I will first give a brief historical overview and explain what the Quantum Hall Effect is and its significance. Then I will discuss the famous result by Thouless, Kohmoto, Nightingale and Den Nijs (the TKNN-formula) that is central to the explanation of the Quantum Hall Effect in periodic non-interacting systems. Finally I will talk about some of the mathematical challenges of trying to generalise that result to systems of interacting lattice-fermions.