# Ordinary Configurations in Point-Line Arrangements

## Quentin Dubroff, Rutgers University

## Date and time: 2pm, Friday, December 6, 2019

## 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 ErdÅ‘s which remain open.