Talk #1: Logan Batson
"The density of integers n relatively prime to the integral part of nα"
We discuss the distribution of positive integers n that are relatively prime to the integral part of nα. We demonstrate that the density of such integers is 6/π2 by separating the cases when α is rational from when α is irrational and using some previous results of Vinogradov, Hardy and Wright.
Talk #2: Ismael El Yassini
"Graph-Theoretic Proof of Roth's Theorem on Arithmetic Progressions"
We present a concise overview of the graph-theoretic proof of Roth's theorem, showcasing the use combinatorial arguments to identify arithmetic progressions within subsets of integers. The talk highlights the applicability of the graph-theoretic approach in number theory.
MC 5417