Spin Tunneling in Magnetic Molecules - A Playground for Mathematical Physics Anupam Garg In certain molecular solids containing clusters of magnetic atoms, the spin of a cluster can tunnel from one orientation to another. In the best known example, Fe8 (total spin 10), the tunneling is quenched at specific values of a static magnetic field applied along the hard axis. This effect can be vividly understood in terms of the geometrical phase between interfering spin trajectories. Closer study, however, reveals a surprise. Experimentally, only four quenching points are seen where the geometrical phase would predict ten. The resolution lies in the nature of the spin trajectories as opposed to particle trajectories in the Feynman path integral (and if it were presented here, there would be no reason for you to come to the talk!). More broadly, spin tunneling has provided the impetus for revisiting the semiclassical limit for spin problems. Such problems arise in the study of nuclear and molecular rotors, models for many body effects in nuclei, and various types of magnetic order. We have a better understanding of spin coherent state path integrals, previously ad hoc rules such as J --> J + 1/2 in various formulas, and (after many false starts) a semiclassical approximation to the propagator that is consistent under composition.