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UID:20260602T212019EDT-3076G6g8Gv@132.216.98.100
DTSTAMP:20260603T012019Z
DESCRIPTION:Title: Sharing Pizza in n Dimensions.\n\nAbstract: We introduce
  and prove the n-dimensional Pizza Theorem. Let H be a real n-dimensional 
 hyperplane arrangement. If K is a convex set of finite volume\, the pizza 
 quantity of K is the alternating sum of the volumes of the regions obtaine
 d by intersecting K with the arrangement H. We prove that if H is a Coxete
 r arrangement different from A_1^n such that the group of isometries W gen
 erated by the reflections in the hyperplanes of H contains the negative of
  the identity map\, and if K is a translate of a convex set that is stable
  under W and contains the origin\, then the pizza quantity of K is equal t
 o zero. Our main tool is an induction formula for the pizza quantity invol
 ving a subarrangement of the restricted arrangement on hyperplanes of H th
 at we call the even restricted arrangement. We get stronger results in the
  case of balls. We prove that the pizza quantity of a ball containing the 
 origin vanishes for a Coxeter arrangement H with |H|-n an even positive in
 teger.\n	\n	This is joint work with Sophie Morel and Margaret Readdy.\n\nLoc
 ation: 201\, avenue du Président-Kennedy\, PK-4323\, UQAM\, Montréal\n\nWe
 b site : https://lacim.uqam.ca/seminaires\n
DTSTART:20221028T150000Z
DTEND:20221028T160000Z
SUMMARY:Richard Ehrenborg\, University of Kentucky
URL:/mathstat/channels/event/richard-ehrenborg-univers
 ity-kentucky-342836
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