Directions in $AG(2,p)$ and the clique number of Paley graphs

Abstract: The directions determined by a point set are the slopes of lines passing through at least two points of the set. A seminal result of Rédei tells us that at least $(p+3)/2$ directions are determined by $p$ points in $AG(2,p)$. We consider cartesian product point sets, i.e. a set of the form $A \times B \subset AG(2,p)$, where $p$ is prime, $A$ and $B$ are subsets of $GF(p)$ each with at least two elements and $|A||B|

Joint work with Józseff Solymosi and Daniel Di Benedetto.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.

The conference program, list of speakers, and abstracts are posted on the external website.