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# Collection Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme

Organizer(s) Dartyge, Cécile ; Drmota, Michael ; Martin, Bruno ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas
Date(s) 5/22/17 - 5/26/17
00:00:00 / 00:00:00
5 5

## Small sumsets in continuous and discrete settings

Also appears in collection : Exposés de recherche

Given a subset A of an additive group, how small can the sumset $A+A = \lbrace a+a' : a, a' \epsilon$ $A \rbrace$ be ? And what can be said about the structure of $A$ when $A + A$ is very close to the smallest possible size ? The aim of this talk is to partially answer these two questions when A is either a subset of $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, $\mathbb{R}$ or $\mathbb{T}$ and to explain how in this problem discrete and continuous setting are linked. This should also illustrate two important principles in additive combinatorics : reduction and rectification. This talk is partially based on some joint work with Pablo Candela and some other work with Paul Péringuey.

### Citation data

• DOI 10.24350/CIRM.V.19171603
• Cite this video de Roton Anne (5/24/17). Small sumsets in continuous and discrete settings. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19171603
• URL https://dx.doi.org/10.24350/CIRM.V.19171603

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