Welcome to the reading class on modelling topological phases of matter. I offered this course in the winter term 2018–19 and recorded it for the benefit of a few students who could not attend in person. I prepared lecture notes for this course. Together with the recorded classes, this should make this material quite suitable for self-study. The course is intended for mathematics students and starts with a crash course on the quantum physics background. The mathematical tools that I use are comparatively basic. In particular, you need not know about C*-algebras and their K-theory. I use the language of homotopy theory instead to formulate the classification.

Date | Topic and Recording Link |
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17.10.2018 | Introduction Physics crash course I |

24.10.2018 | Physics crash course: rotations, projective representations, anti-unitary symmetries |

7.11.2018 | No recording available |

24.11.2018 | Band theory: Spectrum of a Schrödinger operator with bounded periodic potential |

21.11.2018 | continuity of eigenvectors and eigenfunctions in band theory tight binding models graphene (begun) |

28.11.2018 | The graphene model |

5.12.2018 | The models by Semenoff, Haldane, Bernevig–Hughes–Zhang, and Su–Schrieffer–Heeger |

12.12.2018 | Homotopy of invertible Hamiltonians |

19.12.2018 | A crash course in homotopy theory |

9.1.2019 | Some basic homotopy theory |

16.1.2019 | More basic homotopy theory |

23.1.2019 | Homotopy classification for Hamiltonians with symmetries |

30.1.2019 | Bulk-edge correspondence in one dimension index and winding number |