Workshop on Invariant Random Subgroups

summary

The purpose of this talk would be to explain the construction of non-discrete locally compact groups with no non-trivial uniformly recurrent subgroups and no non-trivial invariant random subgroups. These groups are defined as groups of piecewise affine homeomorphisms of a locally compact Cantor space. Some examples can also be viewed as subgroups of the group AAut(T) of almost automorphisms of a regular tree, but unlike AAut(T), they are not compactly generated. Joint work with Nicolas Matte Bon.