TU Berlin Fakultät II
Institut für Mathematik

Geometry II (SoSe 16)



Geometry Group



Vergangene Semester


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Geometry II:
Discrete Differential Geometry

(Summer 2016)

Lectures John M. Sullivan Mon 08:30–10:00 MA 841
Mon 10:15–11:45 MA 841
Tutorials Hanka Kouřimská Wed 10.15–11.45 MA 851
Thur 08.30–10.00 MA 851

This is a basic course of the Berlin Mathematical School and lectures will be held in English.


Beginning next week, Hanka's office hours will be offered only by appointment.
Exams for this course are available 25–27 July
The 9th sheet has been updated! It now contains 3 tasks with a maximum of 16 points.
There was a typo in exercise 2. Also, Hanka will not be at the university the next week, 20-24 June. There WILL be tutorials, but there will be NO OFFICE HOURS during that week. As a replacement, Hanka will offer an additional session of office hours the following Monday, 27 June, from 11.45 to 13.15. The due date for the handing in of the (eigth) exercise sheets will thus move from the lecture on 27 June to the tutorials, i.e. 29 June, 10.15 and 30 June, 8.30. This change holds only for that week! The exercise sheets number seven and nine are expected to be handed in on Mondays between the lectures, as usual.
There was another typo in the hint for exercise 3. The ansatz should be y'=sinh(t), sorry for that! The sheet has been updated accordingly.
Additional information was added to exercise 2 in the 4th sheet! Also, some typos were removed.
Oral exams for last semester's courses will be offered on 20 May, 3 June and 10 June. Exact exam dates for this course in the week of 25–28 July will be announced soon.
Prof. Sullivan's office hours had been listed incorrectly; they will be Thursdays 13:30–14:30. However today is an exception: office hours today will be 14:30–15:30.
Hanka's office hours will take place on weekly basis starting next week. This week there are NO office hours on Wednesday (Hanka will not be at her office at that time). Feel free to send her an email and set an appointment if you need to talk to her.


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, 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 handed in in groups of two people.
  • The homework is due weekly on Mondays in the break between lectures.
  • Exams will be offered the last week of July 2016 and then again in May 2017.

Office Hours

Office hours John Sullivan Thur 13:30–14:30 MA 802
Hanka Kouřimská Wed 12:00–13:30 MA 863

Hana Kourimska . 19.07.2016.