The research project of John Harer is concerned with three major topics: The first topic is the homology of the mapping class group and related groups such as the Torelli group and the level-n mapping class groups. The second topic is the Reshetikhin-Turaev invariant of a 3- manifold and the associated representations of the mapping class groups. The third is an attempt to find an automatic structure for the mapping class group. (This is joint with S. P. Kerckhoff of Stanford University.) The study of 3-manifolds is a very natural geometric pursuit. We live in one, ignoring the time dimension, so it could even have cosmological implications.
