Spectral Analysis of the Volume Operator in Loop Quantum Gravity
  We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat generic vertices of valence greater than four. It is found that the vertex geometry characterizes the volume spectrum. 
J. Brunnemann and D. Rideout