Speaker: Orit Raz (TAU)

Title: On sets defining few ordinary lines

Abstract:
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The Dirac--Motzkin conjecture is the statement that, for $n$ large, a set
$P$ of $n$ points in the plane not all lying on a line spans at least $n/2$
ordinary lines (i.e., lines passing through exactly two points of $P$).

In 2013, Green and Tao confirmed this long standing conjecture, and in fact
provided a more precise version of the bound, for large $n$. Moreover, they
proved a structure result, characterizing the extremal examples.

In the talk I will review the result and sketch parts of the proof.