these-carr

UNIVERSITÉ PIERRE ET MARIE CURIEThèse de doctoratSpécialité : Mathématiquesprésentée parSarah CARRet soutenue à Paris le 27 juin 2008Pour obtenir le grade deDOCTEUR de l’UNIVERSITÉ PIERRE ET MARIE CURIEMultizeta values: Lie algebras and periods onM0,n-Valeurs multizêta : algèbres de Lie et périodes surM0,nDirectrice de thèse JuryLeila SCHNEPS (CNRS) Daniel BERTRAND (Univ. Paris VI)Jacky CRESSON (Univ. Pau)Hidekazu FURUSHO (Nagoya Univ.)Pierre LOCHAK (CNRS)HOANG NGOC MINH (Univ. Lille)RapporteursLeila SCHNEPS (CNRS)Don ZAGIER (Collège de France, MPIM)Don ZAGIER (Collège de France, MPIM)Masanobu KANEKO (Kyushu Univ.)ABSTRACTMultizeta values: Lie algebras and periods onM0,nSarah CarrLeila Schneps, AdvisorThis thesis is a study of algebraic and geometric relations between multizeta values.There are many such known sets of relations, coming from different theories, which areconjecturally equivalent to each other and which conjecturally describe all relations onmultizeta values. This thesis was inspired by the conjectures of equivalence of theserelations.To study the algebraic relations, we begin by looking at the double shuffle Lie al gebra associated to multizeta values, which encodes the double shuffle relations. Inchapter 2 of this thesis, we prove a result which gives the dimension of the associateddepth graded pieces of the double shuffle Lie algebra in depths 1 and 2, thus verifyingthe conjecture that the double shuffle Lie algebra is ...