TU Berlin Fakultät II
Institut für Mathematik

Geometry II



Geometry Group



Vergangene Semester


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Geometry II:
Discrete Differential Geometry

(Summer 2018)

Lectures John M. Sullivan Wed 08:15–09:45 MA 841
Thu 14:15–15:45 MA 848
Tutorials Isabella Retter Mon 10:15–11:45 MA 644

This is a basic course of the Berlin Mathematical School and lectures will be held in English. The tutorials will be held in English or German, depending on the students attending each one.


          For  the derivation of the Euler-Lagrange eq.I recommend to have a look into V.I.Arnold, Mathematical Methods of Classical Mechanics, Springer, 2nd ed., p. 55 ff. (or take a copy in the lecture tomorrow)
There is no lecture on Wed 18 Apr; the first lecture will be on Thursday 19 April.
There are no tutorials on Mon 16 Apr; tutorials and office hours will start in the second week.


Classical differential geometry studies smooth curves and surfaces, for instance in terms of their curvatures. This course will consider analogous notions and results for discrete (usually polygonal) curves and discrete (usually polyhedral) surfaces. Specific topics will include:

  • Curvatures of discrete curves, discrete elastic curves
  • Curvatures of discrete surfaces, special parametrizations and classes of surfaces
  • Discrete conformal and harmonic maps, the discrete Laplace operator, Delaunay triangulations, circle packings, discrete conformal equivalence, discrete Riemann surfaces, variational principles


Exercise sheets

Homework policy and exam information

  • To get a certificate for the tutorial and thus qualify to take the oral exam, you need to satisfactorily complete 60% of the homework assignments.
  • The exercises are to be done in groups of two people and handed in at one of the tutorials each Monday.
  • Oral exams will be offered in the first week after the end of lectures, July 23rd-27th, and again in October, around the beginning of the winter semester.

Office Hours

Office hours John Sullivan Mondays, 13:00–14:00 MA 802
Isabella Retter Thursdays, 09:15-11:00
MA 866

Isabella Retter . 18.05.2018.