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Multi angle Small sumsets in continuous and discrete settings

Auteurs : de Roton, Anne (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Codes MSC :
    11B13 - Additive bases, including sumsets
    11B75 - Combinatorial number theory
    11B83 - Special sequences and polynomials

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 01/06/17
      Date de captation : 24/05/17
      Collection : Research talks
      Format : MP4
      Durée : 00:41:55
      Domaine : Number Theory ; Combinatorics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2017-05-24_de_Roton.mp4

    Informations sur la rencontre

    Nom du congrès : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme
    Organisteurs Congrès : Dartyge, Cécile ; Drmota, Michael ; Martin, Bruno ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas
    Dates : 22/05/17 - 26/05/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1595.html

    Citation Data

    DOI : 10.24350/CIRM.V.19171603
    Cite this video as: de Roton, Anne (2017). Small sumsets in continuous and discrete settings. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19171603
    URI : http://dx.doi.org/10.24350/CIRM.V.19171603

    Voir aussi


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