The Yang-Mills measure and quantization.

The Kauffman bracket skein algebra of a surface F is a quantization
of the SU(2)-characters of the fundamental group of F with respect to
Goldman's Poisson structure. Integration with respect to the
symplectic measure quantizes to a diffeomorphism invariant trace on
the skein algebra. We use the unitary properties of the 6j-symbols of
U_q(sl_2) to prove the existence of the trace,
and I give a shadow world form for evaluating it. (This work was joint with
Doug Bullock and Joanna Kania-Barotszynska.)