Measured Group Theory, Percolation and Non-Amenability
Event details
| Date | 01.10.2015 |
| Hour | 17:15 › 18:15 |
| Speaker | Damien Gaboriau (CNRS, ENSL, Université de Lyon) |
| Location | |
| Category | Conferences - Seminars |
Amenability for groups is a concept introduced by J. von Neumann in his seminal article (1929) tin connection with the so-called Banach-Tarski paradox. It is easily shown that the free group F on two generators is non-amenable. It follows that the countable discrete groups containing F are non-amenable. von Neumann's problem examines whether the converse holds true. In the 80's Ol'shanskii showed that his Tarski monsters lead to counter-examples. However, in order to extend certain results from groups containing F to any non-amenable countable group G, it may be enough to know that G contains F in a more dynamical sense.
Namely, it may be sufficient to find a probability measure preserving free action of G whose orbits contain the orbits of some free action of F.
The solution to this ``measurable von Neumann's problem'' involves percolation theory on Cayley graphs, measured laminations by subgraphs and some invariants of dynamical systems. I will present an introduction to this subject, with some examples, pictures, and movies. We may even take this opportunity to start a ping-pong game...
Namely, it may be sufficient to find a probability measure preserving free action of G whose orbits contain the orbits of some free action of F.
The solution to this ``measurable von Neumann's problem'' involves percolation theory on Cayley graphs, measured laminations by subgraphs and some invariants of dynamical systems. I will present an introduction to this subject, with some examples, pictures, and movies. We may even take this opportunity to start a ping-pong game...
Links
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Valérie Krier