Normal generators for mapping class groups are abundant

We'll begin by giving an introduction to mapping class groups of surfaces, which play an important role in low-dimensional topology, geometric group theory, and other fields. We'll then describe a number of simple criteria that ensure that a mapping class group element is a normal generator, that is, its normal closure is the whole group. We apply these criteria to show that almost every periodic element is a normal generator whenever genus is at least 3.  We also show that every pseudo-Anosov element with stretch factor less than √2 is a normal generator. Our pseudo-Anosov results answer a question of Long from 1986. This is joint work with Dan Margalit.