Title: Maximal subgroups of finite simple groups and applications

Lecturer: 
Colva Roney-Dougal
University of St Andrews 

The Classification of Finite Simple Groups was one of the major
achievements of 20th century mathematics. Given the resulting list of
groups, the natural next questions are to ask about their properties:
their subgroup structure, representation theory, permutation actions
etc. This course will start with a brief introduction to the groups
themselves, and then go on to present various results describing their
subgroup structure. For some of the families of finite simple groups
we have very detailed results, whereas for others many open problems
still remain. We will then see how these results can be applied to a
range of other questions about arbitrary finite groups, and in
particular to questions about random generation.