Algorithms in Group Theory
This seminar will cover algorithms in the context of Group Theory. We will analyse the mathematical theory needed for solving concrete mathematical problems and will implement algorithms in GAP.
A few talks will be given during the semester. After the lectures finished we will hold a block seminar for the remaining talks as well as the practical exercises.
You will have to implement algorithms in GAP, document your code properly and give a talk of 90 minutes about your algorithms.
This is a preliminary list of possible topics:
- Algorithms for dealing with elliptic curves
- Backtrack Algorithms to decide whether two permutations are conjugate in the symmetric group
- Jordan- and Frobenius normal forms over arbitrary fields.
- Bruhat decomposition in the special linear group
- Subgroup ladders in permutation groups
- Simplicial surfaces
You are welcome to propose topics yourself. We will try to cover them during this seminar.