I will define Weyl n-algebras and explain how they may be used to construct such invariants of 3-manifolds and knots as
Axelrod-Singer invariants, perturbative Chern-Simons invariants and the Kontsevich integral.
I will explain how to calculate the Kontsevich integral of the unknot by means of this construction.
The talk is based on two papers:
arXiv:1504.01931
and arXiv:1509.03415.
Besides, I hope to discuss some possible further applications and generalizations.