Entry in the Vorlesungsverzeichnis VVZ.
Mobius transformations and hyperbolic geometry.
There is a forum where you can ask and answer questions.From time to time, a script will appear here, but this will generally be a few weeks behind the lecture. Script (Version July 20, final version).
The lecture takes place Tue 11:15 - 12:00 in HG D 3.2 and Thu 14:15 - 16:00 in HG G5.
| Tue, 11:15-12:00 | Thu, 14:15 - 16:00, | Fri |
|---|---|---|
| 21. Feb. Introduction | 23. Feb. Class cancelled | Sheet 1, Solutions 1 |
| 28. Feb. Orientation and Similarities | 2. Mar. Möbius transformations | Sheet 2, Solutions 2 |
| 7. Mar. The Möbius transformations form a group | 9. Mar. The matrix approach | Sheet 3, Solutions 3 |
| 14. Mar. Generators of the Möbius transformations | 16. Mar. Cayley transformation | Sheet 4, Solutions 4 |
| 21. Mar. Rotation group | 23. Mar. Clines | Sheet 5, Solutions 5 |
| 28. Mar. Clines | 30. Mar. Conformal maps | Sheet 6, Solutions 6 |
| 4. Apr. Conformal maps | 6. Apr. Möbius transformations preserving the disk | |
| Easter break | Sheet 7, Solutions 7 | |
| No exercise class on monday 17. Apr. (box in HG J68 for hand-ins) 18. Apr. Möb(B1) acts transitively, the Apollonian slide |
20. Apr. More Möb(B1) | Sheet 8 (Correction: Ex 3a, t < 1) Solutions 8 |
| 25. Apr., Triple transitivity, a correction | 27. Apr., Cross ratio | Sheet 9, Solutions 9 |
No exercise class on monday 1. May (box in HG J68 for hand-ins) 2. May, Cross ratio is preserved under Möbius transformations. |
Extra exercise class/Q&A on Wednesday May 3., 16:00 - 18:00, HG F 26.3 4. May, The hyperbolic metric. |
Sheet 10, Solutions 10 |
| 9. May, the hyperbolic metric. | 11. May, the acosh formula | Sheet 11, Solutions 11 |
| 16. May, | 18. May, No class |
Sheet 12, Solutions 12 |
| 23. May, | 25. May | |
No exercise class on monday 29. May (box in HG J68 for hand-ins) 30. May, |
Extra exercise class/Q&A on Wednesday May 31., 16:00 - 18:00, CHN G 46 1. June |
The exercise classes take place on Monday 16:15 - 18:00. The exercise sheets appear on Friday (week n). On Monday (in week n+1) the sheets may be discussed during the class (best look at it before, but don't solve it yet). One week later (week n+2) the sheets can be handed in in the exercise class on Monday (or alternatively in the box in HG J 68). The exercises will then be corrected and returned the next Monday (week n+3). While not mandatory, solving exercises is an integral part of learning and strongly encouraged.
The first exercise class will take place Monday, 27.02.2023. Exercise classes can be chosen on mystudies until then.| Time | Room | Tutor | Language | |
|---|---|---|---|---|
| Group 1 | Mo 16-18 | HG D3.2 | Eva Soares | en |
| Group 2 | Mo 16-18 | HG F 5 | Benjamin Reinhard | en |