Harvard Math Picture Language Seminar: Determining distributions of groups from their moments
MATHEMATICAL PICTURE LANGUAGE, SEMINARS
Melanie Wood - Harvard University
Just as moments of a distribution of real numbers are a powerful tool that (if they are not too large) determine the distribution uniquely, we can consider certain averages as moments of a distribution of groups (or more general algebraic structures). We discuss how these moments determine a distribution of groups uniquely, and how that can be applied to find distributions of fundamental groups of random 3-manifolds, fundamental groups of curves over finite fields, and to give conjectures for distributions of important groups arising in number theory such as class groups.