Exact Results in Quantum Theory

Wigner 6j symbols are defined in terms of recoupling theory for representations of SU(2). They exhibit surprising connections to the geometry of tetrahedra and disctete 3d gravity (Regge action) in the large 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) extension to the case of quantum SU_q(2), where similar asymptotics are also known.