Small sumsets in continuous and discrete settings | Vidéo | Carmin.tv

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Small sumsets in continuous and discrete settings

By Anne de Roton

Appears in collections : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme, 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.

Information about the video

Date of recording 24/05/2017
Date of publication 01/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19171603
Cite this video de Roton, Anne (24/05/2017). 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

Domain(s)

Bibliography

de Roton, A. (2016). Small sumsets in real line : a continuous $3k-4$ theorem. <arXiv:1605.04597> - https://arxiv.org/abs/1605.04597

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