Spencer Unger (University of Toronto)

Descriptive Dynamics and Combinatorics Seminar

Title: circle squaring

Abstract: We show that a closed disk and square with the same area are equidecomposible with  pieces. A simple argument implies that the pieces are also . Indeed the argument takes advantage of closure properties of the class of sets that are both  and . More generally, we show that if  and  have the same positive Lebesgue measure and small boundary, then they are equidecomposible with pieces that are countable unions of finite Boolean combinations of translates of ,  and open sets. This is joint work with Narmada Varadarajan and Felix Weilacher.

Zoom meeting https://mcgill.zoom.us/j/87587975637