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SUMMARY:Bernard Lidický (Iowa State University)
DTSTART:20211129T140000Z
DTEND:20211129T150000Z
DTSTAMP:20260423T035406Z
UID:EPC/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/79/">Max
 imum number of almost similar triangles in the plane</a>\nby Bernard Lidic
 ký (Iowa State University) as part of Extremal and probabilistic combinat
 orics webinar\n\n\nAbstract\nA triangle $T'$ is $\\varepsilon$-similar to 
 another triangle $T$ if their angles pairwise differ by at most $\\varepsi
 lon$. Given a triangle $T$\, $\\varepsilon >0$ and $n \\in \\mathbb{N}$\, 
 Bárány and Füredi asked to determine the maximum number of triangles $h
 (n\,T\,\\varepsilon)$ being $\\varepsilon$-similar to $T$ in a planar poin
 t set of size $n$. We show that for almost all triangles $T$ there exists 
 $\\varepsilon=\\varepsilon(T)>0$ such that $h(n\,T\,\\varepsilon)=(1+o(1))
 n^3/24$. Exploring connections to hypergraph Turán problems\, we use flag
  algebras and stability techniques for the proof. This is joint work with 
 József Balogh and Felix Christian Clemen.\n
LOCATION:https://researchseminars.org/talk/EPC/79/
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