Atiyah-Hirzebruch spectral sequence in the band theory
- October 24 at 16:00 - 18:10, 2019 (JST)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.
The topological nature of the band theory in crystalline systems can be well described by the topological K-theory over the Brillouin zone torus. In the first part of my talk, I will present the band-theory understanding of the grading of the K-group, and how the exactness axiom and the Mayer-Vietoris sequence are naturally understood. In the second part, I discuss how to compute the differentials of the Atiyah-Hirzebruch spectral sequence associated with a cell decomposition.