Sums of algebraic dilates

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• Jeck Lim (Oxford)
• Thursday 05 March 2026, 14:30-15:30
• MR13 (EL.05).

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Let $\lambda_1,\ldots,\lambda_k$ be algebraic numbers. We show that $$|A+\lambda_1\cdot A+\dots+\lambda_k\cdot A|\geq H(\lambda_1,\ldots,\lambda_k)|A|-o(|A|)$$ for all finite subsets $A$ of $\mathbb{C}$, where $H(\lambda_1,\ldots,\lambda_k)$ is an explicit constant that is best possible. In this talk, we will discuss the main tools used in the proof, which include a Frieman-type structure theorem for sets with small sums of dilates, and a high-dimensional notion of density which we call “lattice density”. Joint work with David Conlon.

This talk is part of the Combinatorics Seminar series.

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