# 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