Hall 123

The Banach-Tarski paradox and Amenability

Arghya Mondal

IMSc

It is possible to cut a ball into finitely many pieces and
rearrange the pieces to get two ball of the same size as that of the
original. I will prove it. Then the implications for (non) existence of
nice measures on the Euclidean space will be discussed. And finally we'll
see how this motivates the definition of amenability of a group. (When did
groups come into the picture?!)