Werner Nahm (Bonn Univ. and DIAS Dublin):
Conformal
Field Theory and the Bloch Group
Polyhedral groups and their graphs (the ADE series) describe
the most basic realizations of string/M-theory and related quantum field
theories, from the minimal models of rational conformal field theory
to the torus compactifications of M-theory. For the simplest cases they
describe everything, from subfactors and fusion to partition functions.
More complicated cases are described by graphs, too, but very little is
known about their universal properties. Concerning the partitions, the
graphs encode algebraic equations and elements of the Bloch group. It is
conjectured that for the relevant graphs the algebraic equations have
abelian Galois group and the Bloch group elements have finite order.