Instructior: Prof. Dr. Giulia Codenotti
Schedule: We will meet on Wednesdays, 12-14 in the seminar room of Arnimallee 2 (so called Villa).
Topics:
The presentations will be grouped in thematic blocks, each of the blocks consisting of 2-3 presentations. The themes will be related to what we saw in Discrete Geometry 1, but should be presented without assuming much preexisting knowledge. The three blocks are:
- hyperplane arrangements: intersection poset, characteristic polynomial and counting regions
- Gale duality and Zonotopes
- computing triangulations: algorithmic issues and oriented matroids
Resources:
Hyperplane arrangements:
Stanley, an introduction to hyperplane arrangements: https://www.cis.upenn.edu/~cis6100/sp06stanley.pdf
Gale duality and zonotopal diagrams:
- Gruenbaum - Convex polytopes (book, available at the library): Sections 5.4 and 6.3
- McMullen - On zonotopes
Triangulations:
- Pfeifle and Rambau: Computing Triangulations Using_Oriented Matroids
- Rambau, proposition 2.2 in this paper
-
De Loera, Rambau, Santos - Triangulations: Structures for Algorithms and Applications (book available at the library), specifically chapter 4 and section 8.1