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Geometry II: Discrete Differential Geometry (Summer 2017)
Discrete differential geometry takes the concepts and results from the theory of smooth curves and surfaces, and looks for analogs for discrete (polygonal) curves paths) and discrete (polyhedral) surfaces. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systms. A list of topics for the course includes: polyhedral surfaces, intelligent (property preserving) discretizations, quad-surfaces, multi-dimensional nets, orthogonal nets, discrete conformal structure and parametrization, integrable systems, examples in physics and geometry, in particular in projective, Lie, Möbius, Laguerre geometries.
This is a course of the Berlin Mathematical School
held in english or deutsch (depending on the audience).
- [2017, April 26]
There will be no Wednesday tutorials.
- [2017, April 21]
The first tutorial will be on Monday, April 24.
It is not clear yet whether there will be a second tutorial on Wednesdays.
- [2017, May 15]
Correction on Exercise Sheet 03, Exercise 2:
The quadrilaterals are supposed to be non-similar.
- [2017, June 14]
No lectures on June 19 and June 22.
- [2017, June 22]
Correction on Exercise Sheet 08, Exercise 1:
You may assume, that $f$ is circular.
- [2017, July 04]
There will be 10 exercise sheets this semester
with a total number of 120 points.
- exercise sheet 01, due May 04
- exercise sheet 02, due May 11
- exercise sheet 03, due May 18
- exercise sheet 04, due May 29
- exercise sheet 05, due June 01
- exercise sheet 06, due June 08
- exercise sheet 07, due June 26
- exercise sheet 08, due June 29
- exercise sheet 09, due July 06
- exercise sheet 10, due July 13
To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.
The exercises are to be solved in groups of two people.
The homeworks are due weekly at the beginning of the lecture on Thurday.
Late homeworks are accepted only with medical excuse.
- A. Bobenko, Yu. Suris, Discrete Differential Geometry. Integrable
Structure, Graduate Studies in Mathematics, Vol. 98, AMS, 2008