Geometry I (Winter 2019 / 2020)

Contents

Non-euclidean geometry: projective, hyperbolic, Möbius.

This is a course of the Berlin Mathematical School held in english or deutsch (depending on the audience).

News

[2021, January 13]

We will offer exam dates in the second week of March.
You can register with Kati Gabler (gabler@math.tu-berlin.de).
The exams are planned as oral exams at TU Berlin.
We also plan to offer further exam dates in April at the beginning of the summer semester.

[2020, August 17]

The next available date to take your exam will be September 01.
Further dates will be available in February 2021.

[2020, February 10]

The exams will take place on April 20. (canceled)
You can register at the office of Kati Gabler, MA873.

[2020, January 17]

There will be 12 exercise sheets with a total number of 96 points.

[2020, January 17]

No lecture on Monday, January 20.
No office hour on Tuesday, January 21.
You may hand in the 10th exercise sheet until Monday, January 27.

[2019, December 13]

Lecture notes for the part on projective geometry are now online. See below.

[2019, December 02]

There will be no tutorial (December 04) and no new exercise sheet this week.
Exercise sheet 07 will be online on December 09 and due December 19.

[2019, November 19]

No office hour of Jan Techter on November 19.
No tutorials on November 20.
If you have any questions about the exerices you can contact me by email.

[2019, October 15]

See below for the homework policy.
The first exercise sheet will be online on Monday, October 21, and due Thursday, October 31.

[2019, October 01]

First lecture on October 14.
First tutorials on October 23.

Exercise sheets

• exercise sheet 12, due February 06
• exercise sheet 11, due January 30
• exercise sheet 10, due January 23
• exercise sheet 09, due January 16
• exercise sheet 08, due January 09
• exercise sheet 07, due December 19
• exercise sheet 06, due December 05
• exercise sheet 05, due November 28
• exercise sheet 04, due November 21
• exercise sheet 03, due November 14
• exercise sheet 02, due November 07
• exercise sheet 01, due October 31

Homework policy

• To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.
• The exercises are to be solved in groups of two people.
• Your hand-ins have to be stapled together and contain names and matriculation numbers of all members of the group.
  We strongly reccommend you to hand in the homework in readable writing, since unreadable writing will not be graded.
• The homeworks are due weekly on Thursday before(!) the start of the lecture.

Literature

• Lecture notes Geometry I WS16 by Alexander Bobenko
• Blog Geometry I WS12 by Thilo Rörig
• Hitchin, lecture notes on Projective Geometry: Chapters 1&2 (Intro, Proj. Spaces),   3 (Quadrics),   4 (Exterior Algebra),   5 (Klein's Erlanger Program)
• Lecture notes by Boris Springborn
• V. V. Prasolov & V. M. Tikhomirov. Geometry
• Felix Klein. Vorlesungen über höhere Geometrie, Vorlesungen über nicht-euklidische Geometrie.
• Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
• Fuchs & Tabachnikov, Mathematical Omnibus
• Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
• Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
• H. S. M. Coxeter. Non-Euclidean Geometry, Projective Geometry.
• J. W. Cannon, W. J. Floyd, R. Kenyon, R. Parry. Hyperbolic Geometry. In: S. Levy (editor). Flavors of Geometry. Mathematical Sciences Research Institute Publications 31. Cambridge University Press, Cambridge, 1997. Pages 59-115. Download PDF from the MSRI.
• D. V. Alekseevskij, E. B. Vinberg, A. S. Solodovnikov. Geometry of spaces of constant curvature. In: E. B. Vinberg (editor). Geometry II. Encyclopedia of Mathematical Sciences 29. Springer, Berlin, 1993. Pages 1-138.

Office hours