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Tuesday, February 9, 2021

**Abstract:** A triangle $T'$ is $\epsilon$-similar to another triangle $T$ if their angles pairwise differ by at most $\epsilon$. Given a triangle $T$, $\epsilon>0$ and a natural number $n$, Bárány and Füredi asked to determine the maximum number of triangles being $\epsilon$-similar to $T$ in a planar point set of size $n$. We determine this quantity for almost all triangles $T$ and sufficiently small $\epsilon$. Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof. This is joint work with József Balogh and Bernard Lidický.

Please contact Sean at SEnglish (at) illinois (dot) edu for Zoom information.