Geometric progressions in syndetic sets

Abstract: In this talk, we will discuss the presence of arbitrarily long geometric progressions in syndetic sets, where a subset of $\mathbb{N}$ (the set of all natural numbers) is called \emph{syndetic} if it intersects every set of $l$ consecutive natural numbers for some natural number $l$. In order to understand it, we will explain the structure of the set $\{\frac{a}{b}\in \mathbb{N}: a, b\in A\}$ for a given syndetic set $A$.

Title: A question of Bukh on sums of dilates \\ Abstract: There exists a $p<3$ with the property that for all real numbers $K$ and every finite subset $A$ of a commutative group that satisfies $|A+A| \leq K |A|$, the dilate sum \[A+2 \cdot A = \{ a + b+b : a, b \in A\}\] has size at most $K^p |A|$. This answers a question of Bukh.

Joint work with Brandon Hanson.

number theory

Audience: researchers in the topic

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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.

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