  Low-energy transport measurements in Quantum Hall systems have been argued to
be governed by emergent modular symmetries whose predictions are robust against
many of the detailed microscopic dynamics. We propose the recently-observed
quantum Hall effect in graphene as a test of these ideas, and identify to this
end a class of predictions for graphene which would follow from the same
modular arguments. We are led to a suite of predictions for high mobility
samples that differs from those obtained for the conventional quantum Hall
effect in semiconductors, including: predictions for the locations of the
quantum Hall plateaux; predictions for the positions of critical points on
transitions between plateaux; a selection rule for which plateaux can be
connected by low-temperature transitions; and a semi-circle law for
conductivities traversed during these transitions. Many of these predictions
appear to provide a good description of graphene measurements performed with
intermediate-strength magnetic fields.
