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SUMMARY:Equipartitioning measures and functions by k-fans
DTSTART:20101021T171500
DTSTAMP:20261005T021850Z
UID:9b145da276a27373e903c6c5135f2965ed6d7ece7fe436eb7208e51f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Imre Barany\nA k-fan is a point in the plane and k halflines e
 manating from it. I'll explain a few results about equipartitions by k-fan
 s of two or more probability measures\, as well as partitions in other pre
 scribed ratios. This group of questions is motivated by a neat problem of 
 Kaneko and Kano from 1998. One of the results\, which is joint with J Mato
 usek\, says that  given two probability measures in the plane\, there exis
 ts a 4-fan that simultaneously equipartitions them.\n\nA recent question\,
  raised by Nandakumar and Ramanda Rao\, asks that\, given a convex body C 
 in the plane and a positive inetger k\, is there a partition of C into k c
 onvex pieces so that each piece has the same area and the same perimeter. 
 I'll sketch the solution in the case k=3 which is a joint result with P Bl
 agojevic and A Szucs. The methods use equivariant topology with a some ext
 ra geometry and combinatorics.
LOCATION:CM 1 4 https://plan.epfl.ch/?room==CM%201%204
STATUS:CONFIRMED
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