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UID:20250704T171149EDT-7658piXhW3@132.216.98.100
DTSTAMP:20250704T211149Z
DESCRIPTION:Title: A constructive solution to Tarski's circle squaring prob
 lem.\n\nAbstract: In 1925\, Tarski posed the problem of whether a disc in 
 R2 can be partitioned into finitely many pieces which can be rearranged by
  isometries to form a square of the same area. Unlike the Banach-Tarski pa
 radox in R3\, it can be shown that two Lebesgue measurable sets in R2 cann
 ot be equidecomposed by isometries unless they have the same measure. Henc
 e\, the disk and square must necessarily be of the same area. In 1990\, La
 czkovich showed that Tarski's circle squaring problem has a positive answe
 r using the axiom of choice. We give a completely constructive solution to
  the problem and describe an explicit (Borel) way to equidecompose a circl
 e and a square. This answers a question of Wagon. Our proof has three main
  ingredients. The first is work of Laczkovich in Diophantine approximation
 . The second is recent progress in a research program in descriptive set t
 heory to understand how the complexity of a countable group is related to 
 the complexity of the equivalence relations generated by its Borel actions
 . The third ingredient is ideas coming from the study of flows in networks
 . This is joint work with Spencer Unger.\n
DTSTART:20190319T183000Z
DTEND:20190319T193000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Andrew Marks (UCLA) 
URL:/mathstat/channels/event/andrew-marks-ucla-295462
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