Fakultät II
Institut für Mathematik

# Arbeitsgruppe Geometrie

Geometry Group

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# Geometry I (Winter 2014/2015)

 Lectures Tutorials Boris Springborn Mon 12-14 MA 313 Mon 16-18 MA 313 Isabella Thiesen Wed 10-12 MA 650 Thu 12-14 MA 848

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

### Contents

Non-euclidean geometry: spherical, hyperbolic, projective, Möbius, Lie, and Plücker line geometry.

### News

[13.11.2014]
In exercise 2 b) on sheet 4 you should solve for the coordinates of a right-angled triangle with angles and edge lengths taken from exercise 2 a).
[31.10.2014]
There was a factor of 2 missing in one of the identities given as hints for ex 2.3, see updated version.
[30.10.2014]
Here are some hints for the second exercise sheet.
[28.08.2014]
The first lecture will be October 13th.
The tutorials start in the second week (i.e. Wednesday, Oct 22nd).

### 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.
• The homework is due weekly at the beginning of the first lecture on Monday. Late homework is accepted only with a medical excuse.

### Examinations

There will be oral exams at the end of the semester.

### Literature

For this course, there will be a book collection ("Semesterapparat") in the Mathematics Library on the first floor.
• 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.
• Dmitry Fuchs & Serge Tabachnikov. Mathematical Omnibus: Thirty Lectures on Classic Mathematics. American Mathematical Society, Providence, RI, 2007. Preprint.
• 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.
• 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.
(This list is not ordered according to any relevant criteria.)

### Office hours

 Boris Springborn Wed 11-13 MA 871 Isabella Thiesen n.V. n.V. MA 866

 Isabella Thiesen . 27.01.2015.