Szemerédi-Trotter theorem in general finite fields

Ali Mohammadi (Sydney)

Abstract

We say a point is incident to a line if it lies on that line. Let $F$ be a finite field, not necessarily of prime order. We seek to establish non-trivial upper bounds on the number of incidences between sets of points and lines in the plane $F\times F$. In this talk I will discuss the best-known results and some improvements.