Scott Harper

Generating infinite simple groups

Famously, every finite simple group can be generated by just two elements, and there is a huge literature demonstrating that much more is true. However, much less is known about the generation of infinite simple groups. In this talk, I will focus on the class of finitely generated simple vigorous groups, which are infinite groups that act on Cantor space in a particularly nice way. Thompson's group V is the motivating example of such a group, and the class includes the various generalisations of this group and many others beside. These groups can all be generated by two elements and this talk will highlight the variety of much stronger things that can be said, along with some applications of these results. This is joint work with Bleak, Donoven and Hyde.