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 for the topics for the term-end paper can be found here. To get credits, please pick at least one, and submit it to the UTokyo LMS page linked below. The deadline is January 30 (Fri), 2026, 23:59.
The histogram of the submission times relative to the deadline in the lectures I did in the past can be found here: Record of submission times. It's interesting to see that people always submit very close to the deadline!
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 | ... | |
| 9. | Dec. 11 | ... | |
| 10. | Dec. 18 | Differential forms and de Rham cohomology 1 | |
| 11. | Dec. 25 | Differential forms and de Rham cohomology 2 | |
| * | Jan. 1 | no class due to New Year Holidays | |
| 12. | Jan. 8 | (Co)homology theories over Z or Z2, I | |
| 13. | Jan. 15 | (Co)homology theories over Z or Z2, II | |
| 14. | Jan. 22 | Characteristic classes I | |
| 15. | Jan. 29 | Characteristic classes II |
email: yuji.tachikawa_at_ipmu.jp