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# Documents  Malvenuto, Claudia | enregistrements trouvés : 8

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## Taming the coloured multizetas Ecalle, Jean | CIRM H

Post-edited

Research talks;Dynamical Systems and Ordinary Differential Equations;Number Theory

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.

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 ...

11M32

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## Algebraic combinatorics, resurgence, moulds and applications (CARMA). Volume 2Marseille # June 26-30, 2017 Chapoton, Frédéric ; Fauvet, Frédéric ; Malvenuto, Claudia ; Thibon, Jean-Yves | European Mathematical Society 2020

Congrès

- 383 p.
ISBN 978-3-03719-205-4

IRMA lectures in mathematics and theoretical physics , 0032

Localisation : Colloque 1er étage (MARS)

opérade # algèbre de Hopf # combinatoire algébrique # moule # renormalisation # période # valeur zêta multiple # fonction résurgente # calcul extraterrestre # champ vectoriel # difféomorphisme

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## Algebraic combinatorics, resurgence, moulds and applications (CARMA). Volume 1Marseille # June 26-30, 2017 Chapoton, Frédéric ; Fauvet, Frédéric ; Malvenuto, Claudia ; Thibon, Jean-Yves | European Mathematical Society 2020

Congrès

- 344 p.
ISBN 978-3-03719-204-7

IRMA lectures in mathematics and theoretical physics , 0031

Localisation : Colloque 1er étage (MARS)

opérade # algèbre de Hopf # combinatoire algébrique # moule # renormalisation # période # valeur zêta multiple # fonction résurgente # calcul extraterrestre # champ vectoriel # difféomorphisme

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## Quantum geometry and resurgent perturbative/nonperturbative relations Dunne, Gerald | CIRM H

Multi angle

Research talks;Number Theory;Mathematical Physics

Certain quantum spectral problems have the remarkable property that the formal perturbative series for the energy spectrum can be used to generate all other terms in the entire trans-series, in a completely constructive manner. I explain a geometric all-orders WKB approach to these perturbative/non-perturbative relations, which reveals surprising connections to number theory and modular forms.

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## Free post-Lie algebras, the Hopf algebra of Lie group integrators and planar arborification Manchon, Dominique | CIRM H

Multi angle

Research talks;Algebra;Combinatorics;Lie Theory and Generalizations;Mathematical Physics

The Hopf algebra of Lie group integrators has been introduced by H. Munthe-Kaas and W. Wright as a tool to handle Runge-Kutta numerical methods on homogeneous spaces. It is spanned by planar rooted forests, possibly decorated. We will describe a canonical surjective Hopf algebra morphism onto the shuffle Hopf algebra which deserves to be called planar arborification. The space of primitive elements is a free post-Lie algebra, which in turn will permit us to describe the corresponding co-arborification process.
Joint work with Charles Curry (NTNU Trondheim), Kurusch Ebrahimi-Fard (NTNU) and Hans Z. Munthe-Kaas (Univ. Bergen).
The two triangles appearing at 24'04" and 25'19'' respectively should be understood as a #.
The Hopf algebra of Lie group integrators has been introduced by H. Munthe-Kaas and W. Wright as a tool to handle Runge-Kutta numerical methods on homogeneous spaces. It is spanned by planar rooted forests, possibly decorated. We will describe a canonical surjective Hopf algebra morphism onto the shuffle Hopf algebra which deserves to be called planar arborification. The space of primitive elements is a free post-Lie algebra, which in turn will ...

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## Connected chord diagrams, bridgeless maps, and perturbative quantum field theory Yeats, Karen | CIRM H

Multi angle

Research talks;Combinatorics;Mathematical Physics

Rooted connected chord diagrams can be used to index certain expansions in quantum field theory. There is also a nice bijection between rooted connected chord diagrams and bridgeless maps. I will discuss each of these things as well as how the second sheds light on the first. (Based on work with Nicolas Marie, Markus Hihn, Julien Courtiel, and Noam Zeilberger.)

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## Combinatorics of Feynman integrals Broadhurst, David | CIRM H

Multi angle

Research talks;Combinatorics;Mathematical Physics

Very recently, David Roberts and I have discovered wonderful conditions imposed on Feynman integrals by Betti and de Rham homology. In decoding the corresponding matrices, we encounter asymptotic expansions of a refined nature. In making sense of these, we appear to have some refuge in resurgence.

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## Produits et coproduits des fonctions quasi-symétriques et de l'algèbre des descentes Malvenuto, Claudia | Departement de Mathematiques Et Informatique;Université du Québec 1994

Ouvrage

ISBN 978-2-89276-132-0

Publications du laboratoire de combinatoire et d'informatique mathématique , 0016

Localisation : Ouvrage RdC (MALV)

algèbre de Hopf # bigèbre des descentes # composition et partition # congruence plastique # coproduit dans Sym # fonction quasi-symétrique # fonction symétrique # évacuation de graphe étiqueté

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