Algebra Seminar: Zsuzsanna Dancso -- Kashiwara-Vergne solutions degree by degree

Zsuzsanna Dancso (University of Sydney) will be speaking this week in the algebra
seminar.  We will go out for lunch after the talk.  

When: Friday 17 May, 12-1pm 

Where: SMRI Seminar Room, Macleay Building (A12) Room 301 

Title: Kashiwara-Vergne solutions degree by degree 

Abstract: The Kashiwara–Vergne (KV) problem was originally posed in the context of
convolutions on Lie groups in 1978, and has wide implications from Lie theory to
harmonic analysis.  The first general solution was found in 2006, by Alekseev and
Meinrenken.  Later, Alekseev–Torossian reformulated the problem as a set of two
equations for automorphisms of the degree completed free Lie algebra on two generators.
In this talk we will introduce the Alekseev-Torossian formulation of the KV equations,
and show that solutions can always be extended degree by degree, hence found recursively
to higher and higher precision.  This may be used to simplify the computation of a class
of Drinfel’d associators, which conjecturally comprises all associators.  

This is a report on some of the work I did while on sabbatical last semester, and is
joint with Iva Halacheva, Guillaume Laplante-Anfossi and Marcy Robertson.  The preprint
is at https://arxiv.org/pdf/2310.20420.