The goal of the paper is to explain a harmonic map approach to two geometric problems related to the Torelli map. The first is related to the existence of totally geodesic submanifolds in the image of the Torelli map, and the second is on the rigidity of representation of a lattice of a semisimple Lie group in a mapping class group.
Dedicated to Professor Gopal Prasad on the occasion of his 75th birthday
"Torelli Locus and Rigidity." Michigan Math. J. 72 643 - 654, August 2022. https://doi.org/10.1307/mmj/20217207