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H 3 Taming the coloured multizetas

Auteurs : Ecalle, Jean (Auteur de la Conférence)
CIRM (Editeur )

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flexions ARI-GARI symmetral-symmetril palindromy polar / bisymmetrals symmetry / exchanger singulator / singuland / singulate cannonical / irreducible extremal algebra satellites question of the audience

Résumé : 1. We shall briefly describe the ARI-GARI structure; recall its double origin in Analysis and mould theory; explain what makes it so well-suited to the study of multizetas; and review the most salient results it led to, beginning with the exchanger $adari(pal^\bullet)$ of double symmetries $(\underline{al}/\underline{il}) \leftrightarrow (\underline{al}/\underline{al})$, and culminating in the explicit decomposition of multizetas into a remarkable system of irreducibles, positioned exactly half-way between the two classical multizeta encodings, symmetral resp. symmetrel.

2. Although the coloured, esp. two-coloured, multizetas are in many ways more regular and better-behaved than the plain sort, their sheer numbers soon make them computationally intractable as the total weight $\sum s_i$ increases. But help is at hand: we shall show a conceptual way round this difficulty; make explicit its algebraic implementation; and sketch some of the consequences.

A few corrections and comments about this talk are available in the PDF file at the bottom of the page.

Keywords : uncoloured/bicoloured multizetas; flexions; bimoulds; irreducibles ; ari/gari biari/bigari; swap;
bialternal/bisymmetral; perinomal algebra; singulators/singulands/singulates; mould amplification satellites

Codes MSC :
11M32 - Multiple Dirichlet series and zeta functions and multizeta values

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 06/07/17
    Date de captation : 27/06/17
    Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Number Theory
    Format : MP4 (.mp4) - HD
    Durée : 01:04:50
    Domaine : Number Theory ; Dynamical Systems & ODE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2017-06-27_Ecalle.mp4

Informations sur la rencontre

Nom de la rencontre : Algebraic combinatorics, resurgence, moulds and applications / Combinatoire algébrique, résurgence, moules et applications
Organisateurs de la rencontre : Chapoton, Frédéric ; Fauvet, Frédéric ; Malvenuto, Claudia ; Thibon, Jean-Yves
Dates : 26/06/17 - 30/06/17
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1599.html

Citation Data

DOI : 10.24350/CIRM.V.19190003
Cite this video as: Ecalle, Jean (2017). Taming the coloured multizetas. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19190003
URI : http://dx.doi.org/10.24350/CIRM.V.19190003

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