Measurable circle squaring

12 May 2015
Oleg Pikhurko
In 1990 Laczkovich proved that, for any two sets $A$ and $B$ in $\mathbb{R}^n$ with the same non-zero Lebesgue measure and with boundary of box dimension less than $n$, there is a partition of $A$ into finitely many parts that can be translated by some vectors to form a partition of $B$. I will discuss this problem and, in particular, present our recent result with András Máthé and Łukasz Grabowski that all parts can be made Lebesgue measurable.
  • Combinatorial Theory Seminar