XXXII Workshop on Geometric Methods in Physics 30.06-6.07.2013

Armen Sergeev

Magnetic Bloch theory and noncommutative geometry

We present an interpretation of magnetic Bloch theory in terms of
noncommutative geometry by providing a ''vocabulary'' which allows
to formulate properties of magnetic Schr\"odinger operator in terms
of $C^*$-algebras.

As an application of this noncommutative version of Bloch theory we
derive a mathematical interpretation of the quantum Hall effect in
terms of noncommutative geometry. Namely, using the ''vocabulary''
of noncommutative geometry, we to construct a cyclic cocycle which
integrality is responsible for the quantization of Hall
conductivity. This construction is due to Kordyukov--Mathai--Shubin.

Event sponsored by:
Belgian Science Policy Office     PAI          University
of Bialystok
University of Bialystok

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