**Abstract:** I will present some recent speculations^{1} regarding the marginals of the
Chern-Simons path integral measure, as observed on holonomies along
embedded trivalent graphs. We will find that there is a simple and
appealing axiomatic description for thereby inspired "consistent
systems of marginals", which involves the Mobius band, the tetrahedron,
hour glasses, and ring around the rosie dances. While the possible
existence of such systems of marginals is at best shaky, we will
explain that they do exist in a perturbative sense (where they provide
a clean and elegant framework for Drinfel'd's theory of associators),
and in a representation theoretic sense (where they relate to the
theory of quantum *6j*-symbols). At the very end, I will explain
how we^{2} got there and why we care.

This abstract is at http://www.math.toronto.edu/~drorbn/Talks/UCSD-000113/.

^{1}
The term "speculations" will be defined at the start of the talk.

^{2}
Dylan Thurston and myself, though the former should not be held
liable for the nonsense.

Transparencies: Disclaimer.jpg, Pentagon.jpg.