PHDTE00012 Experimental Topology
In this course, we will explore surfaces, higher-dimensional manifolds and more general complexes from a triangulation point of view.
Our main focus will be on
- constructions (of extremal or otherwise interesting examples),
- tools (e.g., discrete Morse theory, homology computation, finite group presentations),
- combinatorial properties (such as face numbers, colorings and valence conditions),
- algorithmic aspects (of how to compose/decompose and to recognize triangulations),
- enumerative methods (in an isomorphism-free way)
- and applications (in material sciences).
We will see that almost all algorithmic problems in topology are hard to solve or even are unsolvable -- yet we will discuss random approaches that allow to settle some of these problems.
Our constructions and examples will cover, among other, equivelar surfaces, Seifert 3-manifolds, knotted triangulations, homotopy 4-spheres, non-PL spheres, random complexes, valence restricted triangulations and polycrystalline materials such as metals and steel.
Skills: Usage of computer tools and experimental approaches to construct or analyze specific examples.
Competences: Ability to combine the theoritical background with applications.
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesOral examination without preparation time
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
Two internal examiners
Criteria for exam assesment
The student must in a satisfactory way demonstrate that she/he has mastered the learning outcome of the course.