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Geometry II:
Discrete Differential Geometry
(Summer 2018)


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.
News
 [15.5.]
For the
derivation of the EulerLagrange 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)
 [11.4.]
 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.
Contents
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
References
 Alexander I. Bobenko, Lecture
notes from the Summer 2014 version of this course.
 John M. Sullivan, Curves of Finite
Total Curvature, in Discrete Differential Geometry,
Birkhäuser, 2008, pp. 137–161.
 John M. Sullivan, Curvatures
of Smooth and Discrete Surfaces, in Discrete
Differential Geometry, Birkhäuser, 2008, pp. 175–188.
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 23rd27th, and again in October, around the
beginning of the winter semester.
Office Hours
