Serina Camungol, Department of Pure Mathematics, University of Waterloo
“Two Out of Three Ain’t Bad”
We are all familiar with the Banach-Tarski paradox: Given a solid ball in 3-dimensional space, there exists a finite decomposition of the ball into disjoint sets which can then be put back together in a way that yields two identical copies of the original ball. But why is this possible? Could this have something to do with amenability? Our aim is to provide a brief introduction to amenability. We will state the definition, some history, examples and equivalent criterion for amenability, and discuss why it is that the Banach-Tarski paradox holds.
M3 3103