TU Berlin Fakultät II
Institut für Mathematik

Geometry II (SoSe 15)



Geometry Group



Vergangene Semester


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Geometry II:
Discrete Differential Geometry

(Summer 2015)

Lectures Boris Springborn Tue 12-14 MA 848
Thur 16-18 MA 850
Tutorials Hanka Kouřimská Wed 10-12 MA 848
Thur 08-10 MA 848

This is a course of the Berlin Mathematical School and may be held in English or deutsch (depending on the audience).


As already announced last week in the tutorials, there will be NO TUTORIAL tomorrow, Wednesday the 8th of July. The homework sheets are to be handed in before the tutorial on Thursday the latest!
The eleventh (and last!) homework sheet is online!
In the next two weeks Hanka's consultation hours will be offered only by appointment.
The tenth homework sheet is online!
The ninth homework sheet is online!
The eighth homework sheet is online!
The seventh homework sheet is online! There will be 11 sheets in total, so you need to score the total of 88 points on the sheets to get the Schein :) Good luck!
The sixth homework sheet is online!
The fifth homework sheet is online!
There has been a small mistake on the homework sheet in the third exercise, in the definition of Ψ. The sheet has been corrected :)
The fourth homework sheet is online!
A quick reminder: the next week Thursday is German national holiday (Himmelfahrt), thus there will be neither a lecture nor a tutorial on that day. You are welcome to join the tutorial on Wednesday :) The exercise sheets should be handed in by Wednesday. You have the whole day to do this, until I leave the office. After that there will be no possibility to hand the homework in, so, since I can't tell you exactly when will I be leaving, make sure you do the handing in sooner than later ;) In case of questions stop by or write me an email.
The third homework sheet is online!
The second homework sheet is online!
The first homework sheet is online!
The tutorials will begin during the second lecture week, that is, 22nd/23rd of april.
Die Übungen finden erst in der zweiten Vorlesungswoche, d.h. am 22/23.4. statt.
Enjoy your holidays! :D


The aim of this course is to apply the notions and results of the classical differential geometry - mainly the theory of curves and surfaces - to discrete curves - piecewise linear curves - and surfaces - polyhedra. Some of the topics considered are:

  • From theory of discrete curves: Curvature of discrete curves, discrete elastic curves
  • From theory of discrete surfaces: Curvature of discrete surfaces, special parametrizations, classes of surfaces
  • Discrete conformal and harmonic maps: discrete Laplace operator, circle packings, discrete conformal equivalence for triangulations, discrete Riemannian surfaces, variational principles


Exercise sheets

The exercise sheets can be found here.

Homework policy

  • To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.
  • The exercises are to be handed in in groups of two people.
  • The homework is due weekly at the beginning of the tutorials on Wednesday or Thursday.

Office Hours

Office hours Boris Springborn see homepage MA 871
Hanka Kouřimská Tue 10-11.30 MA 863

Hana Kourimska . 07.07.2015.