A milestone in graphene research was the 2005 discovery of an integer quantum Hall effect in this novel carbon-based two-dimensional (2D)  electron system. Contrary to its manifestation in conventional 2D  electron systems, such as in semiconductor heterostructures, the  graphene quantum Hall effect reflects the "ultra-relativistic" character  of the underlying carriers, via a particular sequence of plateaus in the  transverse Hall resistance.
A natural question arises from this discovery: what about the fractional  quantum Hall effect in graphene? Does it also reflect the  ultra-relativistic character of the charge carriers? To what extent is  it different from the fractional quantum Hall effect in  (non-relativistic) semiconductor heterostructures? Many of these  questions remain open from an experimental point of view, although some  fractional states have recently been observed in the two- and  four-terminal configuration.
This talk aims at a theoretical perspective on the fractional quantum  Hall effect in graphene, namely in view of its multi-component character  due to the fourfold spin-valley degeneracy, which is approximately respected by the underlying electron-electron interactions. This theoretical perspective will be confronted with recent experimental  advances.