Geometry II: Discrete Differential Geometry (Summer 2013)

This is a course of the Berlin Mathematical School held in English.

News

[03.07.]

There will be no tutorials on Wed 03.07. and Thu 04.07. due to illness.

[18.06.]

There will be no office hours tomorrow 19.06. from 16-17h.

[22.05.]

Exercise sheet 6 will only be available tomorrow 23.05.

[13.05.]

There is a mistake in Exercise 4.1. The Darboux transform is moving to the left and not to the right. So 1.2 should be T - (1,0) and similarly 1.3.

[06.05.]

There is a mistake in Exercise 3.1, the primes are missing in the definition of the unit tangents. As there is no lecture on May 9, the sheet is due before the next lecture, i.e. May 14.

[30.04.]

Due to public holiday on 1 May and 9 May there will be no tutorials on these days.

[23.04.]

The new exercise sheets will be available Tuesday evening.

[19.04.]

Thursdays tutorial will take place in room EN-180.

[17.04.]

The tutorial on Thu 18.04. 10-12 will be in Room MA 875. This will be only on the 18.04. I will try to find another room for the rest of the semester.

Please fill out this form. This will allow me to contact you via e-mail without needing to type copy the email-adresses by hand. Thank you.

[20.03.]

The first lecture will be on Tuesday 09.04., the first tutorial on Wednesday 17.04.

Contents

This course deals with discrete analogs of smooth differential geometry of curves and surfaces. So the main objects of the course will be discrete curves (polygons) and discrete surfaces (polyhedral surfaces). Potential topics include:

From the theory of curves: discrete tangent flow, discrete tractrix and Darboux transformation, curvature of discrete curves and discrete elastica.

From the theory of surfaces: discrete curvatures, discrete parametrizations and special classes of surfaces, discrete conformal and discrete harmonic maps, discrete Laplace operator, circle patterns and packings, discrete conformal equivalence of triangle meshes and discrete Riemann surfaces, variational principles.

References

• Alexander Bobenko's Geometry II lecture notes
• Ulrich Pinkall's Tractrix applet (java webstart)
• Ulrich Pinkall's Kurven und Flächen lecture notes [German]

Additional material

• Straightforward computational proof for the permutability of Darboux transformations of plane curves

Exercise sheets

Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments. Homeworks may be prepared individually or in groups of two students and are due at the beginning of Thursdays lecture.

Office Hours