Mathai Varghese

Noncommutative geometry and the quantum Hall effect

In this talk, I will dicuss some models of the integer/fractional quantum Hall effect based on noncommutative geometry. While in the case of the integer quantum Hall effect the underlying geometry is Euclidean, a model of the fractional quantum Hall effect, which is based on hyperbolic geometry simulating the multi-electron interactions will be discussed. The fractional values of the Hall conductance is derived as integer multiples of orbifold Euler characteristics, and are compared with experimental data.