Finite Simple subgroups of Exceptional Lie Groups
A 1987 paper by Arjeh Cohen and Bob Griess proposed a list of candidate finite simple subgroups that might embed in exceptional Lie groups. Over the next 15 years the status of all these candidate subgroups was resolved in papers of Cohen, Griess, Kleidman, Lisser, Ryba, Serre and Wales. Recent work of Craven and Litterick on maximal subgroups of finite groups of Lie type has raised the more delicate question of the classification of embeddings up to conjugacy. In this talk, I will explain the origins of the Cohen-Griess list and the various strategies used to verify it. In particular, I will discuss the mainly computational strategies that I applied to construct particular embeddings. I will then describe recent work with Darrin Frey and Moty Katzman to settle certain conjugacy problems.