Workshop on Invariant Random Subgroups

Lecture 1: Lie groups and their parabolic subgroups, measured actions, Margulis factor theorem implies normal subgroup theorem;

Lecture 2: IRS in Lie groups and relation with pmp actions, “Borel density” for IRS, statement of the Stück–Zimmer theorem and application to IRSs in higher rank groups;

Lectures 3/4: cocycles, factor theorem of Nevo–Zimmer, proof of the Stück–Zimmer theorem;

Lectures 4/5: Proof of the Nevo–Zimmer factor theorem;

Lecture 6: IRSs in higher rank p-adic Lie groups.

Robert Zimmer, Ergodic theory and semisimple groups, Birkhäuser, copy here.

Garrett Stück, Robert Zimmer, Stabilizers for ergodic actions of higher rank semisimple groups, Annals of math. 1994, copy here.

Amos Nevo, Robert Zimmer, A generalization of the intermediate factors theorem, J. d'analyse math. 2002, copy here.

Arie Levit, The Nevo–Zimmer intermediate factors theorem over local fields, Geom. Ded. 2017, Arxiv preprint.