Program
The Matrix Group Recognition Project
Introduction
- General introduction and motivation
- Basic algorithms for matrix operations
- Black Box groups, oracles and Straight line programs
- Random elements in Black Box groups
- Theory of algorithms (Monte Carlo, Las Vegas), complexity
- Summary algorithms for permutation groups
Part I
- Aschbacher's Theorem
- Constructive recognition and standard generators
- The Composition Tree model
- The Black Box model
- Algorithms for the Aschbacher classes
- Centralisers of involution, Bray trick
- Maximal subgroups of classical groups
- Other algorithms to compute in matrix groups
- Verification
Part II
- Proportions of elements in symmetric groups
- Proportions of elements in classical groups
Slides
Lectures by Max Neunhoeffer
Lectures by Alice Niemeyer
- Black-Box Groups, Oracles and more
- Algorithms for Permutation groups
- Recognition of Classical Groups of Lie Type
- Estimating proportions of elements