This site contains the information on the master course on symplectic geometry that I teach in the Fall term 2026 in Lyon. Information about the master program can be found here. You can provide anonymous feedback on the lectures here.

If you want to receive emails concerning the lectures please register here.

Session log

Final exam : 09. December, 9:45, building ‘Quai 43’, room 112

Tenth session : 02. December, 9:45, building ‘Quai 43’, room 112

Ninth session : 25. November, 9:45, building ‘Quai 43’, room 113

Eighth session : 18. November, 9:45, building ‘Quai 43’, room 113

Seventh session : 11. November, 9:45, building ‘Quai 43’, room 112

Partial exam : 04. November, 9:45, building ‘Quai 43’, room 112

Planned duration: 2.5 hours (i.e., 150 minutes)

No sessions on 21. and 28. October

Sixth session : 14. October

In the beginning of the session we did a little overview of what we have learned so far, which is not in the lecture notes.

Fifth session : 07. October

In addition to the material of the lecture notes, we discussed how the smooth real-valued functions on a manifold are a Fréchet space. This is not exam-relevant.

Fourth session : 30. September

In addition to the material in the lecture notes, we have discussed how the de Rham differential on $\mathbb R^3$ gives rise to the gradient, the curl and the divergence. We have not fully discussed the tensor algebra in the lecture, however it is in slightly more detail in the lecture notes.

  • Some people asked for a reference for interesting things on topological vector spaces related to products. Here are the lecture notes by Michael Heins I mentioned. (NOT RELEVANT FOR THE LECTURE)

  • A nice elementary explanation of tensor products is given here and a slightly more advanced one here.

Third session : 23. September

In the lecture notes the example for the Serre-Swan theorem (functions vanishing at a point of the circle) is worked out; in the lecture, part of it was posed as an exercise.

Second session : 16. September

In addition to the material in the lecture notes, we discussed how to define the Moebius vector bundle and show that it is not trivial. (The category theory part at the end was already done in lecture one and will be continued in lecture three)

First session : 09. September

In addition to the material in the lecture notes, we have discussed what a category is; notes on this will be added to the lecture notes after lecture two.

Lecture notes

Here are the current lecture notes: PDF.

Exams

There will be a partial and a final written exam:

  • A partial exam (CP) will take place on 04. November. You can take a cheat sheet (one-sided) into the exam. Click here for a mock exam showing what type of exercises will be in the partial exam.

  • The final exam (CT) will be during the usual lecture time on 09. December. You can take a cheat sheet (two-sided) into the exam.

The final grade will be $\max(CT , 0.3\cdot CP + 0.7\cdot CT)$

Organizational

  • We will have 10 sessions (ca. 2.5 hours each)
  • Here is a map of the Lyon 1 (la Doua) campus.

Contact

  • You can send me an email (leonid@ryvkin.eu)
  • Alternatively you can leave a comment below (using your github account)