Invariable generation of Thompson groups

A subset S of a group G invariably generates G if for every choice of $g(s)\in G$ ,$s\in S$ the set ${s^g(s):s\in S}$ is a generating set of G. We say that a group G is invariably generated if such S exists, or equivalently if S=G invariably generates G. In this talk, we study invariable generation of Thompson groups. We show that Thompson group F is invariably generated by a finite set, whereas Thompson groups T and V are not invariable generated. This is joint work with Tsachik Gelander and Kate Juschenko.