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\titlehead{KV and DS Lie algebra in mould theory}
\authorhead{Nao Komiyama}
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\begin{document}

\title{On Kashiwara-Vergne Lie algebra and double shuffle Lie algebra in mould theory}

\author{Nao Komiyama \\
Department of Mathematics, Graduate School of Science \\
Osaka University \\
Osaka, Japan, 560-0043 \\
\url{komiyama.nao.aww@osaka-u.ac.jp}}

\date{}

\maketitle

\begin{abstract}
In 2012, Schneps (\cite{Sch12}) showed that there exists an embedding between the double shuffle Lie algebra introduced by Racinet (\cite{Rac}) and the Kashiwara-Vergne Lie algebra introduced by Alekseev and Torossian (\cite{AT}).
In the proof of this embedding, a relation called the {\it senary relation} is used, which is a notion introduced in Ecalle's study (\cite{E}) of multiple zeta values using mould theory.
On Lie algebras and embeddings above, bigraded or elliptic versions have also been studied (\cite{FK}, \cite{RS}).
In my talk, I will explain the above topics and recent topic (\cite{Sch25}) as much as time permits.
\end{abstract}

%\section{Introduction}
%
%In the paper \cite{CholeskyWork:2006} $\ldots$

\begin{thebibliography}{99}

%\bibitem{CholeskyWork:2006}
%Claude Brezinski.
%\newblock The life and work of {A}ndr\'e {C}holesky.
%\newblock {\em Numer. Algorithms}, 43:279--288, 2006.

\bibitem{AT}
A. Alekseev and C. Torossian, 
\newblock The Kashiwara–Vergne conjecture and Drinfeld's associators,
\newblock {\em Ann. Math.}, 175 (2012), no. 2, p. 415-463.

\bibitem{E}
J. Ecalle,
\newblock The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of multizeta irreducibles,
\newblock {\em Asymptotics in dynamics, geometry and PDEs. Generalized Borel summation. Vol. II}, 2011, p. 27-211.

\bibitem{FK}
H. Furusho and N. Komiyama,
\newblock Kashiwara-Vergne and dihedral bigraded Lie algebras in mould theory,
\newblock {\em Ann. Fac. Sci. Toulouse Math}, (6) 32 (2023), no. 4, 655–725.

\bibitem{Rac}
G. Racinet, 
\newblock Doubles mélanges des polylogarithmes multiples aux racines de l'unité,
\newblock {\em Publ. Math. Inst. Hautes Études Sci.}, No. 95 (2002), 185–231.

\bibitem{RS}
E. Raphael and L. Schneps,
\newblock On linearised and elliptic versions of the Kashiwara-Vergne Lie algebra,
\newblock 2017, https://arxiv.org/abs/1706.08299v1.

\bibitem{Sch12}
L. Schneps, 
\newblock Double shuffle and Kashiwara-Vergne Lie algebras,
\newblock {\em J. Algebra 367}, 2012, p. 54-74.

\bibitem{Sch25}
L. Schneps, 
\newblock The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra,
\newblock 2025, https://arxiv.org/abs/2504.14293.

\end{thebibliography}

\end{document}
