Program

The Matrix Group Recognition Project

Introduction

1. General introduction and motivation
2. Basic algorithms for matrix operations
3. Black Box groups, oracles and Straight line programs
4. Random elements in Black Box groups
5. Theory of algorithms (Monte Carlo, Las Vegas), complexity
6. Summary algorithms for permutation groups

Part I

1. Aschbacher's Theorem
2. Constructive recognition and standard generators
3. The Composition Tree model
4. The Black Box model
5. Algorithms for the Aschbacher classes
6. Centralisers of involution, Bray trick
7. Maximal subgroups of classical groups
8. Other algorithms to compute in matrix groups
9. Verification

Part II

1. Proportions of elements in symmetric groups
2. Proportions of elements in classical groups

Slides

Lectures by Max Neunhoeffer

1. What can we do with matrices (over finite fields)?
2. Aschbacher's Theorem
3. The MeatAxe

Lectures by Alice Niemeyer

1. Black-Box Groups, Oracles and more
2. Algorithms for Permutation groups
3. Recognition of Classical Groups of Lie Type
4. Estimating proportions of elements

Lectures by Eamonn O'Brien

1. Basic concepts
2. Constructive recognition
3. The Composition Tree