This talk concerns the paper "Homomorphisms from mapping class groups" by William Harvey and Mustafa Korkmaz, available from the arXiv. The main result of this paper is that any homomorphism from the mapping class group Mod_g of a connected closed orientable surface of genus g to Mod_h is trivial if g is at least 3 and h < g. This result provides further illustration of the deep analogy between arithmetic groups and mapping class groups first suggested by Harvey and establishes the analog for surface mapping class groups of a recent result of Bridson-Vogtman for the automorphism groups of free groups.