Ordinary Configurations in Point-Line Arrangements

Place: CUNY Graduate Center, Rm 5383

The Sylvester-Gallai theorem states that every finite planar point set $P$, not contained in a single line, must span a line containing exactly two points of $P$. Such a line is called an ordinary line. One can ask whether there must exist $r>2$ points of $P$ such that each line determined by them is ordinary or if similar results hold for higher degree curves such as conics. In this talk, I will survey a number of recent results in this direction, discussing standard techniques as well as some related problems of Erdős which remain open.