Geometry I: Analytic and Projective Geometry (Winter 2012)

This is a course of the Berlin Mathematical School held in English.

News

[2.5.2013]

The next dates for Oral Exams in Geometry I are Friday 31.05. and 05.07.2013. You can register for the exam in the secretary's office (Mathias Kall, MA 873).

[11.4.2013]

The next date for Oral Exams in Geometry I is Friday 03.05.2013. You can register for the exam in the secretary's office (Mathias Kall, MA 873) starting from Monday 15.04.2013.

[14.3.2013]

The next date for Oral Exams in Geometry I is Thursday the 21.03. You can register for the exam in the secretary's office (Mathias Kall, MA 873). Other dates will be offered during the semester.

[13.2.2013]

Please read the blog entries about the end of term get-together and shifted office hours.

[31.1.2013]

Next week, Emanuel's office hours will be shifted from Monday 4.2. 10:30-12:00 to Wednesday 6.2. 12-14.

[13.1.2013]

In exercise 9.1 it is to show that the scalar product of p and q is less or equal to -1 (not 1).
(The exercise sheet has been updated accordingly)

[7.1.2013]

In exercise 8.3. one should not consider skew hexagons as they are defined, but instead talk about non-planar hexagons.

Hint: From the fact that a hexagon is non-planar, you can deduce that some of the extended edges are skew. Which ones? For some pairs of extended edges, this is not clear and the existence of further intersection points is related to the question, whether the hexagon is contained in a quadric of signature (++--)...

(The exercise sheet has been updated accordingly)

[23.11.2012]

Emanuel's office hours have been changed to Monday, 10:30 - 12:00

[19.11.2012]

In exercise 3 of the 4th exercise sheet, it has to be n > 1.
(The exercise sheet has been updated accordingly)

[14.11.2012]

Please participate in the doodle poll about changing Emanuel's office hours to Monday.

[8.11.2012]

In exercise 3 of the 3rd exercise sheet, one should assume that the point P is not contained in the hyperplane h.
(The exercise sheet has been updated accordingly)

[8.11.2012]

Two lectures in December will be held in different rooms than usual:
Monday 10.12. in MA 649
Thursday 13.12. in MA 650

[24.10.2012]

The first exercise sheet is online.

[17.10.2012]

The first lecture is now online.

Contents

Euclidean and non-euclidean geometry: projective, hyperbolic, Möbius, and maybe Lie geometry. The continuation is Geometry II: Discrete Differential Geometry.

Exercise sheets

Homework policy

To get a certificate of participation, you need to satisfactorily complete 60% of the homework assignments.

The exercises are to be solved in groups of two people.

The homeworks are due weekly at the beginning of the lecture on Thursday. No homework will be accepted after the deadline has passed.

Lecture notes / Blog

The idea is to interactively create lecture notes using a blog. Each homework group of students is responsible to write up a lecture once during the semester and publish it as a post in our blog.

To be registered as a user for the blog, please write an email to Emanuel (huhnen[at]math.tu-berlin.de) that contains your desired username (minimum 4 characters, only lower case letters and numbers) and the email address you want to use for the blog. An account will be created for you and you will receive an invitation email to join the blog.

Exam / Grading

At the end of the semester, oral exams will be offered.

Literature

• Lecture notes by Boris Springborn
• V. V. Prasolov & V. M. Tikhomirov. Geometry. Translations of Mathematical Monographs, 200. American Mathematical Society, Providence, RI, 2001.
• Nigel Hitchin's lecture notes on Projective Geometry.
• Felix Klein. Vorlesungen über höhere Geometrie. Grundlehren der Mathematischen Wissenschaften, 22. Springer-Verlag, Berlin, 1968.
• Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
• Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
• Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
• H. S. M. Coxeter. Non-Euclidean Geometry. Mathematical Association of America, Washington, DC, 1998.

Office Hours