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SUMMARY:Sums of algebraic dilates - Jeck Lim (Oxford)
DTSTART:20260305T143000Z
DTEND:20260305T153000Z
UID:TALK245272@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:Let $\\lambda_1\,\\ldots\,\\lambda_k$ be algebraic numbers. We
  show that\n$$|A+\\lambda_1\\cdot A+\\dots+\\lambda_k\\cdot A|\\geq H(\\la
 mbda_1\,\\ldots\,\\lambda_k)|A|-o(|A|)$$\nfor all finite subsets $A$ of $\
 \mathbb{C}$\, where $H(\\lambda_1\,\\ldots\,\\lambda_k)$ is an explicit co
 nstant that is best possible. In this talk\, we will discuss the main tool
 s used in the proof\, which include a Frieman-type structure theorem for s
 ets with small sums of dilates\, and a high-dimensional notion of density 
 which we call "lattice density". Joint work with David Conlon.
LOCATION:MR13 (EL.05)
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