Friday, 7 December 2018
(Not in this seminar series, but perhaps of interest to its
participants:)
10:00am M Sabok (McGill) (CIRGET)
Circle squaring and actions of Zn
Location: PK-5115, Président-Kennedy Building,
UQAM
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 Zn that lies behind this recent result. This is joint work
with T. Ciesla.