Geometry II (Summer 2022)

This is an Advanced Course of the Berlin Mathematical School (BMS) and will be held in English.

Content

• Non-Euclidean Geometries and Klein's Erlangen program:
  Möbius geometry, Laguerre geometry, Lie geometry, Plücker geometry.
• Topics of Discrete Differential Geometry

Exercises

• Exercise Sheet 01
• Exercise Sheet 02
• Exercise Sheet 03
• Exercise Sheet 04
• Exercise Sheet 05
• Exercise Sheet 06
• Exercise Sheet 07
• Exercise Sheet 08
• Exercise Sheet 09
• Exercise Sheet 10
• Exercise Sheet 11

Literature

• Lecture notes (work in progress)
• Springborn, old (but partially updated) lecture notes from the 2007 version of the course "Geometry I" at TU Berlin
• Prasolov & Tikhomirov, Geometry, TMM 200, Amer. Math. Soc.
• Hitchin, lecture notes on Projective Geometry, Chapters 1 Introduciton, 2 Proj. Spaces ,   3 Quadrics,   4 Exterior Algebra,   5 Klein's Erlanger Program
• Fuchs & Tabachnikov, Mathematical Omnibus
• Klein, Vorlesungen über höhere Geometrie, GMW 22, Springer
• Blaschke, Projektive Geometrie, Birkhäuser
• Berger, Geometry I & II, Springer
• Audin, Geometry, Springer
• Coxeter, Non-Euclidean Geometry, Math. Assoc. Amer.
• Cannon, Floyd, Kenyon & Parry, Hyperbolic Geometry, from Flavors of Geometry, MSRI
• Martin, The Foundations of Geometry and the Non-Euclidean Plane, UTM, Springer
• Henderson, Experiencing Geometry, Prentice Hall
• Blaschke, Thomsen: Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. III, Differentialgeometrie der Kreise und Kugeln, 1929
• Cecil, Lie Sphere Geometry: With Applications to Submanifolds
• Elie Cartan, Theory of Spinors.
• Sulanke, Projective and Cayley-Klein Geometries

Office hour

• Jan Techter: Mon 13-14, MA 880