Amenability of finitely generated groups

The notion of amenability was introduced by John von Neumann in 1929 in his work on the Banach-Tarski paradox. This very interesting property turns out to be related to various areas of mathematics, such as measure theory, representation theory, geometry, probability theory and more – giving way to a number of equivalent reformulations, some of them conjectural. We will discuss amenability in relation to the algebraic structure of a (finitely generated) group, as well as to such geometric and probabilistic properties as growth, random walks and percolation.