organisation de l'atelier "IRS à Sète" pour l'ANR AGIRA
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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.
ref. Arxiv preprint
The purpose of this talk would be to investigate IRS's in groups acting on rooted trees, in particular the group of finitary automorphisms of a d-ary rooted tree. We exploit the p.m.p. action of these groups on the boundary of the tree to understand fixed point sets of ergodic IRS's. We show that in the fixed point free case IRS's behave like the ones in the Nevo-Stück-Zimmer world, but if there are fixed points they resemble the ones in Vershik's theorem on the finitary permutation group. Joint work with László Márton Tóth.