Data:	Mercoledì 23 Novembre 2011, h. 16:30
Luogo:	Dip. Matematica, Univ. Roma "La Sapienza"
Speaker:	Damien Gaboriau, Università di Lione
Titolo:	Measured Group Theory, Percolation and Non-Amenability
Abstract:	Amenability of groups is a concept introduced by J. von Neumann in his seminal article (1929) to explain the so-called Banach-Tarski paradox. It is easily shown that the non-cyclic free groups F are non-amenable. It follows that the countable discrete groups containing F are non-amenable. The classical von Neumann's problem was asking whether the converse holds true. Inthe 80's Ol'shanskii showed that his Tarski monsters are 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 relax the condition and to know that G contains F in a more dynamical sense. Namely, we would like to construct a probability measure preserving action of G whose orbits can be partitioned into orbits of some ergodic free action of F. The solution to this measurable von Neumann's problem involves percolation theory on Cayley graphs and measured foliations by subgraphs. I will present an introduction to this subject.