  Charge carriers in graphene are chiral quasiparticles ("massless Dirac
fermions"). Graphene provides therefore an amazing opportunity to study subtle
quantum relativistic effects in condensed matter experiment. Here I review a
theory of one of these unusual features of graphene, a "pseudodiffusive"
transport in the limit of zero charge carrier concentration, which is related
to existence of zero-modes of the Dirac operator and to the Zitterbewegung of
unltrarelativistic particles. A conformal mapping technique is a powerful
mathematical tool to study these phenomena, as demonstrated here, using the
Aharonov-Bohm effect in graphene rings with Corbino geometry as an example.
