Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Johannes SINGER - Erlangen,
Titre Shuffle renormalization of (q-)multiple zeta values
Horaire14:00 à 15:00
RésumeMultiple zeta values (MZVs) are multidimensional generalizations of the Riemann zeta function which are usually studied at positive integers. It is a natural question to ask for MZVs defined for non-positive arguments. In dimension greater than one - in contrast to the case of Riemann zeta function - there are tuples of non-positive integers belonging to the pole set of the meromorphic continuation of MZVs. In the talk we study the Hopf algebra of multiple polylogarithms and the corresponding q-analogue at non-positive arguments which are related to the shuffle product of MZVs. In order to obtain renormalized MZVs for all non-positive arguments we apply the procedure of renormalization introduced by Connes and Kreimer in perturbative quantum field theory. This is a joint work with Kurusch Ebrahimi-Fard and Dominique Manchon.