Douglas Lectures

Date: April 2, 2019

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Vaughan Jones, Vanderbilt University

Title: An introduction to subfactors

Abstract: Von Neumann algebras are closed *-algebras of operators on Hilbert space. A factor is a von Neumann algebra whose center is just the scalar multiples of the identity. Murray and von Neumann discovered novel factors in the 1930’s. Among which are the II_1 factors whose Hilbert spaces admit a dimension function. Thus a subfactor N in M has an index [M:N] given by the dimension of M as a Hilbert space over N. A finer invariant is the principal graph of a subfactor, a graph whose norm is the square root of the index. I will list all subfactors of index less than 4 together with their indices and principal graphs.