VL: Discrete Geometry I (Summer 2025)
This is a BMS Area 5 Core Course.
It is accompanied by a seminar, for those who are interested.
The exercise (UE) and tutorial (Tut) sessions will be given by Lena Weis.
| VL: | Tuesday | 10-12 | BH-N 334 |
| Thursday | 12-14 | BH-N 243 |
| UE: | Tuesday | 14-16 | MA 650 |
| Tut: | Wednesday | 10-12 | MA 850 |
- TU's central administration decided to move the course (in time and space) on short notice [7 April 2025], as indicated above!
- Evaluation forms: course and exercises
- There will be an opportunity for oral/portfolio exams on Monday, 21 July, and Tuesday, 22 July. Please send me an email if interested in these dates.
- Why Writing by Hand Is Better for Memory and Learning
Contents
This course is an introduction to polyhedral geometry.
Basic algorithmic concepts in the field are covered, too.
- Convexity
- Polytopes and Polyhedra
- Linear Programming
- Computing Convex Hulls
- Voronoi Diagrams
- Delaunay Triangulations
References
- Joswig: Convex polytopes and linear programs. Snapshots of modern mathematics from Oberwolfach, no.2, 2025.
- Joswig and Theobald: Polyhedral and algebraic methods in computational geometry. Springer, 2013.
- Ziegler: Lectures on polytopes. GTM 152. Springer, 1995.
Code examples
- Tuesday, 20 May 2025: OSCAR, polymake
- Thursday, 19 June 2025: polymake
- Tuesday, 24 June 2025: Graham scan, planar convex hull algorithm, produced by ChatGPT 4o, answering the prompt: "Give me a planar convex hull algorithm, implemented in Julia."