XXXII Workshop on Geometric Methods in Physics | 30.06-6.07.2013 |

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## Armen Sergeev## Magnetic Bloch theory and noncommutative geometryWe 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. |

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University of Bialystok |

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