Alain Valette

The Chabauty space of closed subgroups in a locally compact group

Endowed with the Chabauty topology, the space Sub(G) of closed subgroups of a locally compact group G becomes a compact space with a canonical action of G. The study of Sub(G) was revived those last years.  

In the first talk we will give definitions and several examples (some of them being joint work with Antoine Bourquin). We will then explain how Sub(G) provides natural compactifications of some homogeneous spaces of G. We will illustrate this with G=SL_n(\Q_p) and study the Chabauty compactification of the space of Cartan subgroups of G. (The latter is joint work with C. Ciobotaru and A. Leitner)

In the second lecture we will move to invariant random subgroups (IRS), i.e. G-invariant probability measures on Sub(G), explain how they generalize both lattices in G and probability measure-preserving G-actions, and explain some recent results about IRS’s.