Conférencier: Marcin Sabok, McGill University

Résumé/Abstract: In 1930's Tarski asked if it is possible to divide the unit square into finitely many pieces, rearrange them by translations and get a disc of area 1. It turns out that this is possible and proved by Laczkovich in the 1990's. His decomposition, however, used nonmeasurable pieces and seemed paradoxical. Recently, Grabowski, Mathe and Pikhurko and Marks and Unger showed that such decompositions can be obtained using nice measurable pieces. I will discuss an abstract result in measurable group theory of ergodic actions of the groups Z^n that lies behind this recent result. This is joint work with T. Ciesla.