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H 1 Towers of Ramanujan graphs

Auteurs : Li, Winnie (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : A $d$-regular graph is Ramanujan if its nontrivial eigenvalues in absolute value are bounded by $2\sqrt{d-1}$. By means of number-theoretic methods,infinite families of Ramanujan graphs were constructed by Margulis and independently by Lubotzky-Phillips-Sarnak in 1980's for $d=q+ 1$, where q is a prime power. The existence of an infinite family of Ramanujan graphs for arbitrary d has been an open question since then. Recently Adam Marcus, Daniel Spielman and Nikhil Srivastava gave a positive answer to this question by showing that any bipartite $d$-regular Ramanujan graph has a $2$-fold cover that is also Ramanujan. In this talk we shall discuss their approach and mentionsimilarities with function field towers.

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      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 03/06/14
      Date de captation : 05/06/13
      Collection : Research talks
      Format : quicktime ; audio/x-aac
      Durée : 01:02:47
      Domaine : Number Theory ; Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2013-06-05_Li.mp4

    Informations sur la rencontre

    Nom du congrès : Arithmetic, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisteurs Congrès : Ballet, Stéphane ; Perret, Marc ; Zaytsev, Alexey
    Dates : 03/06/13 - 07/06/13
    Année de la rencontre : 2013
    URL Congrès : http://iml.univ-mrs.fr/ati/conferences/A...

    Citation Data

    DOI : 10.24350/CIRM.V.18582803
    Cite this video as: Li, Winnie (2013). Towers of Ramanujan graphs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18582803
    URI : http://dx.doi.org/10.24350/CIRM.V.18582803