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SUMMARY:Theorems of Caratheodory\, Helly\, and Tverberg without dimension 
 - Imre Bárány (UCL and Rényi Institute)
DTSTART:20181011T140000Z
DTEND:20181011T150000Z
UID:TALK109870@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Caratheodory's  classic result says that if a point $p$ lies i
 n the convex hull of a set $P \\subset R^d$\, then it lies in the convex h
 ull of a subset $Q \\subset P$ of size at most $d+1$. What happens if we w
 ant a subset $Q$ of size $k < d+1$ such that $p \\in conv Q$? In general\,
  this is impossible as  $conv Q$ is too low dimensional. We offer some rem
 edy: $p$ is close to $conv Q$ for some subset $Q$ of size $k$\, in an appr
 opriate sense. Similar results hold for the classic Helly and Tverberg the
 orems as well. This is joint work with Karim Adiprasito\, Nabil Mustafa\, 
 and Tamas Terpai.\n
LOCATION:MR12
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