The slot with the title Mathematical Physics / 数理物理学 in the Graudate School of Physics was dormant for about twenty years. I decided to revive it last year to have an introductory course on algebraic topology meant for theoretical physicists. The rationale is as follows.
In the last ten years, theoretical physicsits realized that algebraic topology is useful and necessary to have a systematic understanding of symmetry-protected topological phases of matter and of anomalies in particle physics. Before that, only a very rudimentary part of algebraic topology was used in theoretical physics. As such, the techniques of algebraic topology required to follow recent advances are not adequately covered in the standard courses of mathematics for physicisists.
This set of lectures is an effort to fill this gap. I plan to use various physics topics to illustrate how concepts from algebraic topology are used.
You'll need to submit the term-end report through the link above. Suggestions to the contents will be provided around the end of December.
2nd slot of Thursdays, from 10:25 to 12:10.
| Date | Summary | Comments | |
|---|---|---|---|
| 1. | Oct. 2 | General introduction to the course | |
| 2. | Oct. 9 | Manifolds 1 | |
| 3. | Oct. 16 | Manifolds 2 | |
| 4. | Oct. 23 | Fiber bundles 1 | . |
| 5. | Oct. 30 | Fiber bundles 2 | |
| * | Nov. 6 | no class due to university schedule | |
| 6. | Nov. 13 | Basic homotopy theory 1 | |
| 7. | Nov. 20 | Basic homotopy theory 2 | |
| * | Nov. 27 | no class due to university schedule | |
| 8. | Dec. 4 | Differential forms and de Rham cohomology 1 | |
| 9. | Dec. 11 | Differential forms and de Rham cohomology 2 | |
| 10. | Dec. 18 | de Rham and other (co)homology theories | |
| 11. | Dec. 25 | Other (co)homology theories and characteristic classes I | |
| * | Jan. 1 | no class due to New Year Holidays | |
| 12. | Jan. 8 | Characteristic classes II | |
| 13. | Jan. 15 | Abelian Chern-Simons terms and the integer quantum Hall effect I | |
| 14. | Jan. 22 | Abelian Chern-Simons terms and the integer quantum Hall effect II |
email: yuji.tachikawa_at_ipmu.jp