# Gabriel Favre: The Banach-Tarski paradox demystified

**Time: **
Fri 2020-02-28 13.15 - 14.15

**Lecturer: **
Gabriel Favre

**Location: **
Kräftriket, house 6, room 306 (Cramér-rummet)

### Abstract

The Banach-Tarski paradox says that any two bounded without empty interior subsets of \(\mathbb{R}^3\) are Isom(\(\mathbb{R}^3\))-equidecomposable. Jargon apart, it means that one can cut a ball into finitely many pieces, move those pieces using rotations and translations (one translation is enough) and get twice the same ball.

The goal of this talk is to handwave how such a phenomenon can occur and to introduce the core mathematical concept behind it: amenability.