Modul: MAT772 Geometrie-Seminar

## Invariant Schreier Structures on Unimodular Random Graphs

Laszlo Marton Toth talk

**Date:** 17.04.19 **Time:** 15.45 - 18.00 **Room:** ETH HG G 43

It is a nice exercise in combinatorics to show that all finite 2d-regular graphs are Schreier graphs of the free group on d generators. We will consider the analogous question in the world of Benjamini-Schramm convergence of sparse graphs. We show that any 2d-regular unimodular random network can be given an invariant random Schreier structure. Connections to Borel combinatorics, measured group theory and Invariant Random Subgroups will also be explored. The talk aims to be self-contained, all important notions will be properly introduced.