A mould-theoretic perspective on Kashiwara-Vergne theory

Diplôme Thèse A mould-theoretic perspective on Kashiwara-Vergne theory eng 2019-09-23 author Raphael Elise 746200 director Alexeev Anton 134019 10.13097/archive-ouverte/unige:127774 urn:nbn:ch:unige-1277746 Sc. 5391 This thesis studies the applications of mould techniques to Kashiwara-Vergne theory. Developed by Jean Ecalle, originally to the purpose of resurgence theory, mould theory proved to be particularly well suited to the study of Multiple Zeta Values. The conjectural isomorphism between the double shuffle and Kashiwara-Vergne Lie algebras naturally led to the transfer of mould techniques from one space to the other. The first chapter is dedicated to presenting the three main spaces: the double shuffle Lie algebra from number theory, the Grothendieck-Teichmüller Lie algebra related to topology and the Kashiwara-Vergne Lie algebra from Lie theory. The second chapter introduces mould theory, using examples linked to the Lie algebras above. It then explains how to translate the defining properties of these spaces into moulds. The third and last chapter is dedicated to the elliptic versions of the Kashiwara-Vergne Lie algebra and contains the main results of this thesis. Dewey 510 25 Section de mathématiques 11 false 848 Groupe de Lie et espaces de modules 12425008-bcda-4fb2-83bb-99d6eadc1b6c Thesis Public phd.pdf 705249 application/pdf openAccess Faculté des sciences / Section de mathématiques

Title	Published in	Access level	OA Policy	Year	Views	Downloads

A mould-theoretic perspective on Kashiwara-Vergne theory				2019	905	1,075

Archive ouverte UNIGE

Raphael, Elise