Ruled surface theory and incidence geometry

Abstract

This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will appear in the book Journey Through Discrete Mathematics, a Tribute to Jiri Matousek, edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springer.