Seminars & Colloquia Calendar

Thomson's problem, which goes back to 1904, asks how N points will arrange themselves on the sphere so as to minimize their electrostatic potential. A more general problem asks what happens for other power law potentials. In spite of quite a bit of experimental evidence accumulated over the past century, and some spectacular results for values of N associated with highly symmetric polyhedra, there have been few rigorous results for the modest case N=5. In my talk I will explain my recent proof that, for N=5, the triangular bi-pyramid is the minimizer with respect to all power laws up to a constant S=15.04808..., and then the minimizer changes to a pyramid with square base. My talk will have some nice computer animations.