Workshop on Invariant Random Subgroups

organisation de l'atelier "IRS à Sète" pour l'ANR AGIRA

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neretin [2018/03/30 11:47]
jraimbau créée
neretin [2018/05/14 17:19] (current)
jraimbau
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 +=== 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 === === Lecture plan ===
  
   * The Neretin group, and why it has no lattices; ​   * 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]]. ​
neretin.1522403272.txt.gz · Last modified: 2018/03/30 11:47 by jraimbau