In this talk, we discuss Green energy and Riesz s-energies on the real, complex, and quaternion projective spaces, as well as the Cayley Plane. We compute the expected Green and Riesz energies of determinantal point processes given by the reproducing kernels of spaces of harmonics, resulting in asymptotic upper bounds for these energies. We also provide asymptotic lower bounds for the Green energies.
The research in this talk is in collaboration with Austin Anderson, Maria Dostert, Peter Grabner, and Tetiana Stepaniuk.