Normal subgroups of mapping class groups

The mapping class group of a surface has an incredibly rich normal subgroup structure. For this reason, a traditional classification theorem for normal subgroups of mapping class groups, in the form of a complete list of isomorphism types, is almost certainly out of reach. However, we might hope to gain some insight via certain invariants of normal subgroups. In this talk, we will view the automorphism group as an invariant of normal subgroups, and give a survey of known examples providing evidence for a conjectured classification of normal subgroups based on recent joint work with Dan Margalit, and including constructions due to Dahmani-Guirardel-Osin and Clay-Mangahas-Margalit.