Beijing Institute of Mathematical Sciences and Applications

Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov

Zhuo Ke Yang

Tuesday, November 26, 2024 4:00 PM - 5:00 PM

A6-101

Zoom 873 9209 0711 (BIMSA)

Weight systems are functions on chord diagrams satisfying the so-called Vassiliev 4-term relations. They are closely related to finite-type knot invariants. Certain weight systems can be derived from graph invariants and Lie algebra.
In a recent paper by M.~Kazarian and the speaker, a recurrence for the Lie algebras~$\mathfrak{so}(N)$ weight systems has been suggested; the recurrence allows one to construct the universal $\mathfrak{so}$ weight system. The construction is based on an extension of the $\mathfrak{so}$ weight systems to permutations.
Another recent paper, by M.~Kazarian, N.~Kodaneva, and the S.~Lando, shows that under the specific substitution for the Casimir elements, the leading term in $N$ of the universal $\mathfrak{gl}$ weight system becomes the chromatic polynomial of the intersection graph of the chord diagram.
In this talk, we establish a similar result for the universal $\mathfrak{so}$ weight system. that is the leading term of the universal $\mathfrak{so}$ weight system also becomes the chromatic polynomial under a specific substitution.
The talk is based on a joint work arxiv: 2411.01128 with Sergei Lando.