Exact Results in Quantum Theory

Wigner 6j symbols are defined in terms of recoupling theory forrepresentations of SU(2). They exhibit surprising connections tothe geometry of tetrahedra and disctete 3d gravity (Regge action) in thelarge spin limit. I will present a simple proof of this fact due to L. Charles by the methods of geometric quantization and explain its (conjectured) extensionto the case of quantum SU_q(2), where similar asymptotics are also known.