Discrete Geometry II, Summer 2016

Michael Joswig, Institut für Mathematik, TU Berlin.

teaching assistant: Benjamin Schröter

Contents

This course covers combinatorial, algorithmic and geometric aspects of polytope theory. Participants should have basic knowledge of polytope theory, e.g. from the lecture "Geometric basics of linear optimization". Here is a tentative list of subjects: convex hull algorithms, Voronoi diagrams, Delaunay decompositions, cure reconstruction, regular subdivisions, secondary fans.

References

1. Beck and Robins: Computing the continuous discretely. UTM. Springer, 2007.
2. De Loera, Rambau and Santos: Triangulations. Springer, 2010.
3. Joswig and Theobald: Polyhedral and algebraic methods in computational geometry. Springer, 2013.
4. Matousek: Lectures on discrete geometry. Springer, 2002.
5. Schrijver: Theory of linear and integer programming. Wiley, 2000.
6. Thomas: Lectures in geometric combinatorics. Student Mathematical Library, 33. IAS/Park City Mathematical Subseries. AMS, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 2006.
7. Ziegler: Lectures on polytopes. GTM. Springer, 1995.

This is a direct link to the books in the library of the Department of Mathematics.

Exercise Sheets

• Tutorial 1
• Tutorial 2
• Tutorial 3
• Tutorial 4
• Tutorial 5 ( a bit polymake code )
• Tutorial 6 - update in Exercies T2
• Here is a perl template file for T4
• Tutorial 7
• Tutorial 8 - update in T1
• Tutorial 9 - correction of formula in T2
• Tutorial 10

polymake

A file with some polymake commands can be foud here. You can load the commands in polymake via "load_commands("FILE")".