=== Presentation ===

The Neretin group of a regular tree is defined as a group of "piecewise automorphisms" on the boundary. It can be endowed with a locally compact topology, and has no lattices. It is a natural question to ask whether it has IRSs beyond the trivial ones. It is likely that a proof that IRSs "parabolic" subgroups  of the Neretin groups (subgroups fixing a point on the boundary of the tree) can be classified using a modification of an argument for  similar groups in the discrete case, and we hope that this might help proving that there are nontrivial IRSs in the Neretin groups. 

=== Lecture plan ===

  * The Neretin group, and why it has no lattices; 
  * Groups acting on trees which have no lattices; 
  * "Parabolic" subgroups and their IRSs: a continuous version of a result of Thomas--Tucker-Drob? 

=== References ===

  * Łukasz Garncarek, Nir Lazarovich, //The  Neretin groups//, [[https://arxiv.org/abs/1502.00991|Arxiv version]]. 
  * Uri Bader, Pierre-Emmanuel Caprace, Tsachik Gelander, Shahar Mozes, //Simple groups without lattices//, Bull. LMS 2012, [[https://arxiv.org/abs/1008.2911|Arxiv version]]. 
  * Adrien le Boudec, //Groups acting on trees with almost prescribed local action//, Comm. Math. Helv. 2016, [[https://arxiv.org/abs/1505.01363|Arxiv version]]
  * Simon Thomas, Robin Tucker-Drob, //Invariant random subgroups of strictly diagonal limits of finite symmetric groups//, Bull. LMS 2014, [[https://arxiv.org/abs/1402.4837|Arxiv version]].