We present formulae for the characters of coset conformal field theories and apply these to specific examples to determine the integer shift of the conformal weights of primary fields. We also present an example of a coset conformal field theory which cannot be described by the identification current method.

We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is paid to simplifications that arise when restricting to a class of initial data which have a certain U(1)×U(1) conformal symmetry.

We show how to connect together the loops of a simple Conformal Loop Ensemble (CLE) in order to construct samples of chordal SLEκ processes and their SLEκ(ρ) variants, and we discuss some consequences of this construction.