Geometry I (Winter 2022 / 2023)

Contents

• Non-Euclidean Geometries and Klein's Erlangen program: projective geometry, hyperbolic geometry, Möbius geometry.
• This is a course of the Berlin Mathematical School held in english.
• Lecture notes for the course will be published on a weekly basis.
• In the tutorials we will introduce and use the python library pyddg and rendering software blender.
• Course registration on ISIS: here.

News

[2022, October 07]

Please register on the courses ISIS page.

[2022, October 05]

During the second lecture, on October 21, we will present the python library pyddg, and help you with the installation.
If possible to you, please bring a laptop.

[2022, October 05]

First lecture on October 17.
First tutorial on October 26.

Literature

• 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.