Abstract. There is compelling evidence including some longroute indirect proofs, that the following are the same, or at least closely and directly related to each other:There is also some weaker evidence that all these topics remain related even when the various commutativity, cocommutativity and other restrictions are dropped.
 The KashiwaraVergne conjecture, which says, more or less, that convolutions of Adinvariant functions on a Lie group are the same as convolutions of Adinvariant functions on its Lie algebra.
 Drinfel'd associators, at least "restricted to one loop", and the work of Alekseev and Torossian.
 Knot invariants, and in particular, the multivariable Alexander polynomial.
 Virtual knots in which overcrossings (but not undercrossings) are made to commute.
 The EtingofKazhdan formalism in the case of cocommutative Lie bialgebras.
If all goes well, in 510 years I will be able to give a coherent explanation of all that (perhaps sooner, if others will get interested and do the work). For now, all I have are some disorganized tidbits.
Partially I will follow the topics and handouts of several talks that I gave recently. In particular, with base:=http://www.math.toronto.edu/~drorbn/Talks, see base/Sandbjerg0810, base/Istanbul0606, base/Zurich080513, base/MSRI0808, and base/Copenhagen081009.
Today's Handout. UVWKnots.html, UVWKnots.pdf.
The Key Points.

