Ruled surface theory and incidence geometry

TL;DR

This paper surveys the application of ruled surface theory in incidence geometry, highlighting key results, methods, open problems, and future research directions in the field.

Contribution

It provides an overview of how ruled surface theory is used in incidence geometry, including recent results and open problems, serving as an expository resource.

Findings

Summarizes key results in incidence geometry using ruled surfaces

Discusses methods and techniques in the field

Identifies open problems and future research directions

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.