On discrete and continuous variants of the distance graph

Abstract: Given ${\Bbb R}^d$ or ${\Bbb F}_q^d$, where ${\Bbb F}_q$ is the finite field with $q$ elements, and a scalar $t$, either in ${\Bbb R}$ or ${\Bbb F}_q$, we can define the distance graph by taking the vertices to be the points in ${\Bbb R}^d$ (or ${\Bbb F}_q^d$) and connecting two vertices $x$ and $y$ by an edge if $$ {(x_1-y_1)}^2+\dots+{(x_d-y_d)}^2=t.$$ Over the past 15 years, the theory of these graphs has undergone rapid development. We are going to describe what is known and the challenges that lie ahead.

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.