"Kashiwara-Vergne solutions degree by degree" (Iva Halacheva, Northeastern University)

12.08.2024 10:00 – 11:00

Solutions to the Kashiwara-Vergne equations (KV solutions) in Lie theory have been shown to play an important role in topology, describing finite-type invariants for a family of knotted objects known as welded foams. The KV solutions come from the degree-completed free Lie algebra on 2 generators, which has a grading, so a natural question that arises is whether, given a solution up to degree n it can be extended to degree n+1. We show this is indeed the case and leads to further interesting properties of the Kashiwara-Vergne groups acting on this set of solutions. This is joint work with Zs. Dancso, M. Robertson, and G. Laplante-Anfossi.

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