Recent interest in the Kashaev–Murakami–Murakami
hyperbolic volume conjecture has made it seem important to be able
to understand the asymptotic behaviour of certain special functions
arising from representation theory — for example, of the quantum
6j–symbols for SU(2). In 1998 I worked out the asymptotic behaviour
of the classical 6j–symbols, proving a formula involving
the geometry of a Euclidean tetrahedron which was conjectured by
Ponzano and Regge in 1968. In this note I will try to explain the
methods and philosophy behind this calculation, and speculate on
how similar techniques might be useful in studying the quantum case.
