Equipe
CALIN
GDR
CNRS Renormalisation
Bures
sur Yvette, les 11 et 12 Mai
2015.
IHES, 35 Route de Chartres 91440 BuressurYvette, France.
Rencontre organisée par Gérard H.E. DUCHAMP, Maxim KONTSEVITCH, Gleb KOSHEVOY et HOANG NGOC MINH
Combinatorics and Arithmetic for Physics : special days
Les algèbres de Hopf combinatoires et diagrammatiques sont des outils efficaces pour la Renormalisation. Les calculs dans ces structures mènent souvent à des problèmes arithmétiques comme des valeurs spéciales des fonctions multiformes, formes modulaires, des identités entre les périodes. Par exemple aussi, la théorie de motifs offre un cadre suffisamment souple pour permettre des interprétations galoisiennes.
In order to facilitate discussions a free lunch will be taken on the spot.
Pour toute réservation (train, hôtel, …), veuillez contacter Monsieur Aimé Bayonga (responsable financier du LIPN  7030 UMR CNRS).
L'inscription est gratuite dans la mesure des places disponibles et il suffit d'envoyer à Aimé Bayonga (avec copies à HNM & GHED) les informations suivantes
Mr/Ms
:
Nom :
Prénom :
institution :
Courriel :
Date
d'arrivée :
Date de départ :
Liste des participants/List of participants
Lundi 11 Mai 09h3010h00 


Accueil des participants 
10h0011h00 
Maxim Kontsevitch

Two word puzzles 
The
first puzzle concerns certain series (similar to the
characteristic polynomial), associated with any element of the
group ring of a group. 
11h0011h30 


pause 
11h3012h30 
David Jarossay 
Multiple harmonic sums, padic multiple zeta values and finite multiple zeta values 
We study multiple harmonic sums, in the framework of the fundamental group of the projective line minus three points. We are interested in particular in their padic aspects. This enables to compute explicitly the padic analogues of multiple zeta values, and to define a geometric notion of "finite multiple zeta values". (slides) 
12h3014h30 


déjeuner 
14h3015h30 
Gleb Koshevoy 
Algebraic and geometric RSK correspondences 
A geometric RSK is a pair of a birational isomporphism of torii and a Laurent polynomial such that their composition is equal to the sum of coordinates. An algebaic RSK is an injective homomorphism a ring of polynomials to the ring of Laurent polynomials, such that there exists a basis of the former ring labeled by points of the valuation cone. A mirror is a case when the valuation cone of an algebraic RSK coincides with the cone of defined by Laurent polynomial for a geometric RSK. We give constructions of geometric and algebraic RSK, and mirrors. 
15h3016h00 


pause 
16h0017h00 
Vincent Rivasseau 
Random tensors 
We shall review recent progress on random tensors using the intermediate field representation. In particular we shall describe in some detail enhanced quartic tensor models of rank four whose single scaling limits can interpolate between continuous random trees and Brownian spheres. (slides) 
Mardi 12 Mai 10h0011h00 
Karol Penson 
Probabilistic and FreeProbabilistic Properties of Canstellation Numbers 
After
a short introduction about the properties of classical Catalan
numbers and their rôle in Physics we shall dwell on a
certain quite vast generalization of Catalan numbers called the
constellation numbers. We solve exactly and explicitly the
Hausdorff moment problem for these numbers and provide explicit
expressions for appropriate positive weight functions. We have
employed the technique of inverse Mellin transform and of
MeijerG functions. For certain values of parameters we analyse
the properties of these solutions from the point of view of free
probability (theorem of Nica and Speicher) and demonstrate their
infinite divisibility with 
11h0011h30 


pause 
11h3012h30 
Dominique Manchon 
The Hopf algebra of finite topologies and mould composition 
In
recent works by L. Foissy, Cl. Malvenuto and F. Patras, a Hopf
algebra structure is constructed on the linear span of all
topologies on the finite sets [n]={1,...,n}. We will describe a
new "internal" coproduct which interacts with the
abovementioned Hopf structure in a precise way. We exhibit a
surjective Hopf algebra morphism L onto WQSym as well as a new
"internal" coproduct on WQSym such that L respects both
internal coproducts. 
12h3014h30 


déjeuner 
14h3015h30 
Vladimir Fock 
Flag configurations, matroids and integrable systems 
We
study the configuration spaces of cyclically ordered flags in a
vector space. On one hand this space has a class of simple
rational (cluster) parameterisations. If we consider infinite
collection of flags in a finite dimensional space and impose
certain discrete symmetry, the the configuration space turn out
to coincide with the space of local 
15h3016h00 


pause 
16h0017h00 
Hoang Ngoc Minh 
Multiplicative Renormalization of Polyzetas and around 
In order to renormalize divergent polyzetas, as well at positive indices as at non positive indices, we establish Abel like theorems for the noncommutative generating series of polylogarithms and of harmonic sums in the factorized form. These allow to draw a precise picture of their structure. (slides) 
17h0017h30 


FIN 
Web talk 
Alin Bostan 
Efficient Experimental Mathematics for Lattice Path Combinatorics 
Classifying lattice walks in restricted lattices is an important problem in enumerative combinatorics. Recently, experimental mathematics has been used to explore and solve a number of difficult questions related to lattice walks. In this talk, we will give an overview of recent results on structural properties and explicit formulas for generating functions of walks in the quarter plane, with an emphasis on the algorithmic methodology. (slides) 
Cyril Banderier (CNRSParis 13), Axel Bacher (Paris 13), Valentin Bonzom (Paris 13), Alin Bostan (INRIA, Saclay), Van Chiên Bui (Paris 13), Stéphane Dartois (Paris 13), Gérard H.E. Duchamp (Paris 13), JeanYves Enjalbert (Paris 13), Vladimir Fock (Strasbourg), Samuel Lelièvre (Paris 11), Sylvia Goodenough (Paris 13), Guadaluppe (), Hoàng Ngoc Minh (Lille 2/Paris 13), David Jarossay (Paris 7), Dmitry Grigoryev (CNRSLille 1), Maxim Kontsevitch (IHES), Gleb Koshevoy (Poncelet Lab, Moscow), Chrsitian Lavault (Paris 13), Lionni Luca (Paris 11), Dominique Manchon (Clermont Ferrand CNRS), Quôc Hoàn Ngô (Paris 13), Nikolay Nikolov (IHES), Karol Penson (Paris 6), Vincent Rivasseau (Paris 11), Pierre Simonnet (Corte), Andrea Sportiello (CNRSParis 13), Adrian Tanasa (Paris 13), Christophe Tollu (Paris 13).