# Mathematics Colloquia and Seminars

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### Spectral theory of the extended Harper's model

**Mathematical Physics & Probability**

Speaker: | Rui Han, UC Irvine |

Related Webpage: | http://www.math.uci.edu/~rhan2/ |

Location: | 1147 MSB |

Start time: | Wed, Feb 1 2017, 4:10PM |

The extended Harperâ€™s model (EHM) describes a 2d crystal with magnetic field perpendicular to the lattice plane. The model generalizes the well-known almost Mathieu operator (or Harperâ€™s equation) by taking into account both nearest and next-nearest neighbor interaction between lattice sites, and was originally popularized by D.J. Thouless.

In this talk we will describe the general spectral decomposition of the EHM as well as recent advances on sharp arithmetic spectral transitions. We will also address results on the measure and the Cantor structure of the spectrum.

Note: room changed back to MSB 1147