We will prove lower bounds for the p-energies of mappings of real, complex and quaternionic projective spaces to arbitrary Riemannian manifolds.  The equality cases of the results for real and complex projective space give strong characterizations of some families of energy-minimizing harmonic mappings of these spaces.  If we have enough time, we will also describe some parallels and possible connections between these results and some theorems and open problems in systolic geometry.

Zoom link: contact Peter McGrath host to get the link.