Title: "What would Galois do? (one analyst's reflections)"
Abstract:
The theory of type II_1 factors has been motivated largely by its many
connections to group theory. In this talk we'll explore just one such
connection, in the study of automorphisms of finite von Neumann algebras.
After giving a short introduction to von Neumann algebras and II_1 factors,
I'll describe two constructions that arise from a group acting on a von Neumann
algebra by outer automorphisms. A recent lemma of Wiggins yields a
proof of a classical "Galois" theorem for a II_1 factor, which relates
subfactors to a lattice of subgroups of automorphisms. This result will be
our entry point into a (not-so-rigorous) discussion of current research on
symmetries of operator algebras. This talk won't assume any
background except some basic algebra, linear algebra, and analysis.