Abstract:
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.
