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 |
|---|---|
| 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 |